Algebra 25

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra   52    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  105    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   30    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  108    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  109    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 29

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(0 1 1 1 1 1 1 0)
(0 1 1 0 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra   56    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  119    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  109    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  118    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 30

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(0 1 1 0 1 1 1 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra   57    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra   25    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  121    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  123    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  124    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 52

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 1)
(1 1 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  181    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   57    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  184    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  185    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 56

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 0)
(1 1 1 0 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra   29    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  195    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  185    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 57

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 1 1)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra   30    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  196    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra   52    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  197    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  200    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 79

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 4, 1, 8, 3 ] 
[ 4, 1, 5 ] 
[ 3, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 1 1 1 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  100    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  260    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  261    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 83

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 4, 3, 8, 1 ] 
[ 8, 1, 4, 3 ] 
[ 3, 8, 1, 4 ] 
[ 1, 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 1 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  104    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   98    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  261    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  270    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 98

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 1 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 4, 3, 1 ] 
[ 3, 8, 2 ] 
[ 1, 4, 3 ] 
[ 2, 3, 8 ] 
[ 4, 3, 8 ] 
[ 8, 2, 3 ] - [ 8, 4, 3 ] 
[ 3, 1, 4 ] - [ 3, 8, 4 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 0 0 0 0 0)
(1 0 1 1 1 1 1 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  306    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  154    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  305    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   83    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 100

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 4, 1, 8, 2 ] 
[ 4, 1, 5 ] 
[ 2, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  105    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra   79    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  316    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  317    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 104

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 4, 2, 8, 1 ] 
[ 8, 1, 4, 2 ] 
[ 2, 8, 1, 4 ] 
[ 1, 4, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  119    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra   83    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  317    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  326    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 105

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 4, 8, 3 ] 
[ 2, 1, 5 ] 
[ 3, 4, 8 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  328    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  100    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra  331    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  332    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 108

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(0 1 1 1 1 1 0 1)
(0 1 1 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  184    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  331    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  123    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  340    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 109

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(0 1 1 1 1 1 1 0)
(0 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  185    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  342    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  343    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra   29    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 118

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 1 1 1 1 1 0 0)
(0 1 1 1 1 1 0 0)
(0 1 1 0 0 0 0 1)
(0 0 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  362    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  361    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   29    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 119

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 8, 4, 2 ] 
[ 8, 4, 3 ] 
[ 3, 8, 4 ] 
[ 2, 1, 4 ] - [ 2, 8, 4 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 0 0 0 0 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  363    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra   29    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  154    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  364    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  362    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  104    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 121

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 5, 2 ] 
[ 4, 8, 3 ] 
[ 5, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 1)
(0 1 1 0 1 1 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 1)
(0 1 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  197    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  125    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra   30    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  372    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  373    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 123

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  108    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  372    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  377    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   30    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  378    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 124

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(0 1 1 0 1 1 1 0)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  200    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  379    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  343    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  373    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  378    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   30    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 125

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 3 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 5, 8, 3 ] 
[ 8, 3, 5 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(0 1 1 0 0 1 1 1)
(0 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  201    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  135    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  121    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra  381    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  382    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  383    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 135

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 3 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(0 1 1 0 0 1 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  211    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  125    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  402    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  403    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  404    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 154

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 3, 8, 4, 2 ] 
[ 8, 4, 2, 3 ] 
[ 4, 2, 3, 8 ] 
[ 2, 1, 4 ] - [ 2, 3, 8, 4 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 1 1 1 1 1)
(0 0 1 1 1 1 1 1)
(0 1 1 1 1 1 1 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  3 -> Algebra   98    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  436    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  433    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  119    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 181

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  328    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra   52    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  196    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  488    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  490    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  491    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 184

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 0 1)
(1 1 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  108    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  490    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  199    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  499    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   52    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 185

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 1 0)
(1 1 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  109    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  501    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  502    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra   56    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   52    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 194

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  118    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  521    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  520    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   56    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 195

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 2, 8, 1 ] 
[ 8, 4, 3 ] 
[ 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  363    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra   56    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  230    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  522    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  521    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 196

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 0 0)
(1 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra   57    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  181    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  523    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  525    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  526    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 197

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 5, 2 ] 
[ 4, 8, 3 ] 
[ 5, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 1 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 1)
(1 1 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  121    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  527    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  201    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra   57    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  529    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 199

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 0 1)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  123    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  525    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  184    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  529    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  534    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   57    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 200

Quiver

[ 2, 1 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 1 0)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  124    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  536    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  502    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   57    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 201

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 3 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 5, 8, 3 ] 
[ 8, 3, 5 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 1 1)
(1 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  125    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  537    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  211    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  197    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra  538    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  539    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  540    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 211

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 3 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 1 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  135    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  558    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  201    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  559    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  560    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  561    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 230

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 4, 2, 3 ] 
[ 2, 3, 8, 4 ] 
[ 4, 2, 3, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 4, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 0 1)
(1 1 1 1 1 1 1 1)
(0 1 1 1 1 1 1 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  4 -> Algebra  592    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  590    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  195    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 260

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 4, 1, 8, 3 ] 
[ 4, 1, 5 ] 
[ 3, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 1 1 0 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  316    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  652    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   79    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  411    permutation [ 2, 3, 1, 5, 7, 6, 8, 4 ]

Algebra 261

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 5, 4, 1 ] 
[ 4, 1, 3 ] 
[ 8, 1, 3 ] 
[ 4, 1, 5 ] 
[ 1, 3, 8 ] 
[ 3, 4, 1 ] - [ 3, 8, 1 ] 
[ 1, 3, 4 ] - [ 1, 5, 4 ] 

Cartan matrix

(1 0 1 1 1 1 1 0)
(1 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 0 0 1 0 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  317    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra   83    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  411    permutation [ 2, 3, 1, 5, 7, 6, 8, 4 ]
vertex  8 -> Algebra   79    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 270

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 4, 3, 8, 1 ] 
[ 8, 1, 4, 3 ] 
[ 3, 8, 1, 4 ] 
[ 1, 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 1 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 0 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra  326    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  305    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  411    permutation [ 2, 3, 1, 5, 7, 6, 8, 4 ]
vertex  6 -> Algebra  671    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   83    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 272

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(1 1 1 1 0 0 0 1)
(1 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  5 -> Algebra  673    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  675    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  676    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 305

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 1 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 4, 3, 1 ] 
[ 3, 8, 2 ] 
[ 1, 4, 3 ] 
[ 2, 3, 8 ] 
[ 4, 3, 8 ] 
[ 8, 2, 3 ] - [ 8, 4, 3 ] 
[ 3, 1, 4 ] - [ 3, 8, 4 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(1 1 1 0 0 0 0 0)
(1 0 1 1 1 1 0 1)
(0 0 1 1 1 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  734    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  433    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  488    permutation [ 1, 4, 2, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra   98    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  270    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 306

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 3, 8, 4, 1 ] 
[ 3, 8, 2 ] 
[ 1, 3, 8, 4 ] 
[ 2, 3, 8 ] 
[ 4, 1, 3, 8 ] 
[ 8, 2, 3 ] - [ 8, 4, 1, 3 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 1 1 1 1)
(1 0 1 1 1 1 1 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra   98    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  734    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 316

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 5, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 4, 1, 8, 2 ] 
[ 4, 1, 5 ] 
[ 2, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  331    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  260    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  758    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  100    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  568    permutation [ 3, 2, 1, 5, 7, 6, 8, 4 ]

Algebra 317

Quiver

[ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 4, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 5, 4, 1 ] 
[ 4, 1, 2 ] 
[ 8, 1, 2 ] 
[ 4, 1, 5 ] 
[ 1, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 1, 2, 4 ] - [ 1, 5, 4 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 1 1 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 0 0 1 0 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  759    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  261    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  104    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  568    permutation [ 3, 2, 1, 5, 7, 6, 8, 4 ]
vertex  8 -> Algebra  100    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 326

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 4, 2, 8, 1 ] 
[ 8, 1, 4, 2 ] 
[ 2, 8, 1, 4 ] 
[ 1, 4, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 1 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra  362    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  270    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  568    permutation [ 3, 2, 1, 5, 7, 6, 8, 4 ]
vertex  6 -> Algebra  777    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  104    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 328

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(1 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  105    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  181    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  779    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  781    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 331

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 4, 8, 3 ] 
[ 2, 1, 5 ] 
[ 3, 4, 8 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(1 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(0 1 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  781    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  108    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  316    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra  789    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  105    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  790    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 332

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 3, 8, 1 ] 
[ 5, 2, 8, 1 ] 
[ 8, 1, 5, 2 ] 
[ 8, 1, 3 ] 
[ 2, 8, 1, 5 ] 
[ 1, 3, 8 ] - [ 1, 5, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 1 1 1)
(1 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  342    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  4 -> Algebra  759    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  7 -> Algebra  790    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  105    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 338

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 1 1 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  497    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  787    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  375    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  340    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  806    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 340

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 1 1 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  499    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  789    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  377    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  108    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  338    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  810    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 341

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 1 1 1 1 1 0 0)
(0 1 1 1 1 1 0 0)
(0 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  811    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  812    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  118    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  810    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  109    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  108    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 342

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 2, 1 ] 
[ 5, 2, 1 ] 
[ 8, 5, 2 ] 
[ 2, 1, 3 ] 
[ 5, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 5, 2 ] 
[ 2, 1, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  404    permutation [ 3, 1, 8, 6, 7, 2, 4, 5 ]
vertex  2 -> Algebra  109    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  813    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  364    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra  811    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  332    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 343

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 3, 2 ] 
[ 2, 5, 4, 3 ] 
[ 3, 2, 5, 4 ] 
[ 4, 3, 2, 5 ] 

Cartan matrix

(1 1 0 1 1 1 1 0)
(0 1 0 1 1 1 1 0)
(0 1 1 0 1 1 1 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  502    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  815    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  109    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  802    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  812    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  124    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 358

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 1 0 0 0)
(0 1 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  517    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  842    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  806    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  841    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  361    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 361

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 1 0 0 0)
(0 1 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  520    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  845    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  810    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  446    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]
vertex  6 -> Algebra  118    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  358    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 362

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 8, 4, 2 ] 
[ 8, 4, 3 ] 
[ 3, 8, 4 ] 
[ 2, 1, 4 ] - [ 2, 8, 4 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 0 1 0 0 0 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  846    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  118    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  433    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  847    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  845    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  119    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  326    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 363

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 8, 4, 3 ] 
[ 1, 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 4, 1, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 1 1 1 1 1)
(0 0 1 0 0 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  119    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  195    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  848    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  846    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 364

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 4, 1 ] 
[ 5, 4, 1 ] 
[ 4, 1, 3 ] 
[ 8, 5, 4 ] 
[ 5, 4, 8 ] 
[ 1, 3, 4 ] - [ 1, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 1 1 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 0 0 0 1)
(1 0 0 1 1 1 1 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  849    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  342    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  850    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  119    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  847    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  759    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 372

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 5, 2 ] 
[ 4, 8, 3 ] 
[ 5, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 2, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 1)
(0 1 0 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  529    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  382    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  123    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  121    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  874    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 373

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 3, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 6, 5, 2 ] 
[ 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(0 1 1 0 1 1 1 0)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra  530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  875    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  876    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  802    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  124    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  874    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  121    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 375

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 1 1 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  532    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  338    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  377    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  880    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 377

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  534    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  340    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  123    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  375    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  883    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 378

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 1 1 0 1 1 0 0)
(0 1 1 0 1 1 0 0)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  884    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  812    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  874    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  883    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  124    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  123    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 379

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 8, 5, 2 ] 
[ 8, 5, 3 ] 
[ 3, 8, 5 ] 
[ 2, 1, 5 ] - [ 2, 8, 5 ] 
[ 5, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 0 1 0 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  885    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  124    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  399    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  815    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  886    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  884    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 381

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 6, 2 ] 
[ 5, 8, 3 ] 
[ 6, 2, 8, 3 ] 
[ 8, 3, 5 ] 
[ 6, 2, 7 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 6 ] 
[ 3, 5, 8 ] - [ 3, 6, 2, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(0 1 1 0 0 1 1 1)
(0 1 1 0 1 1 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(0 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  538    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  384    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra  402    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  125    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  893    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 382

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 5, 8, 3 ] 
[ 8, 3, 5 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 1)
(0 1 1 0 0 1 0 1)
(0 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 1 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  539    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  403    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  372    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  125    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  895    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 383

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 6, 3, 8, 2 ] 
[ 8, 2, 6, 3 ] 
[ 3, 8, 2, 6 ] 
[ 2, 6, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 0)
(0 1 1 0 0 1 1 0)
(0 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  540    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  811    permutation [ 2, 6, 1, 7, 8, 5, 4, 3 ]
vertex  4 -> Algebra  404    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  876    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra  893    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  895    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  125    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 384

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 2 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 2 ] 
[ 8, 3, 2 ] 
[ 6, 8, 3 ] 
[ 8, 3, 6 ] 
[ 3, 2, 7 ] 
[ 2, 7, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 0 1 1)
(0 1 1 0 0 0 1 1)
(0 1 1 0 0 1 0 1)
(0 0 0 1 1 1 0 1)
(0 0 0 0 1 1 0 1)
(0 0 0 0 0 1 0 1)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  541    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  405    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  381    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra  651    permutation [ 3, 1, 2, 8, 6, 4, 5, 7 ]
vertex  8 -> Algebra  668    permutation [ 3, 1, 2, 8, 6, 4, 5, 7 ]

Algebra 399

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 3, 8, 5, 2 ] 
[ 8, 5, 2, 3 ] 
[ 5, 2, 3, 8 ] 
[ 2, 1, 5 ] - [ 2, 3, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 1 1 1 1 1 1)
(0 0 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  4 -> Algebra  437    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  912    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  909    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  379    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 402

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ], [ 4, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 6, 2 ] 
[ 4, 8, 3 ] 
[ 6, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 2, 7 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 6 ] 
[ 3, 4, 8 ] - [ 3, 6, 2, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 1)
(0 1 1 0 0 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  559    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  405    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  5 -> Algebra  381    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  135    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  501    permutation [ 6, 2, 1, 7, 8, 4, 5, 3 ]

Algebra 403

Quiver

[ 1, 2 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 1)
(0 1 1 0 0 1 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  560    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  382    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  135    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  849    permutation [ 2, 7, 1, 6, 8, 4, 5, 3 ]

Algebra 404

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 6, 3, 8, 2 ] 
[ 8, 2, 6, 3 ] 
[ 3, 8, 2, 6 ] 
[ 2, 6, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 1 1 0)
(0 1 1 0 0 1 1 0)
(0 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  561    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  342    permutation [ 2, 6, 1, 7, 8, 4, 5, 3 ]
vertex  5 -> Algebra  383    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  501    permutation [ 6, 2, 1, 7, 8, 4, 5, 3 ]
vertex  7 -> Algebra  849    permutation [ 2, 7, 1, 6, 8, 4, 5, 3 ]
vertex  8 -> Algebra  135    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 405

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 2 ], [ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 6, 8 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 2 ] 
[ 8, 3, 2 ] 
[ 6, 8, 3 ] 
[ 8, 3, 6 ] 
[ 3, 2, 7 ] 
[ 2, 7, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 1 0 0 0 1 1)
(0 1 1 0 0 0 1 1)
(0 1 1 0 0 1 0 1)
(0 0 0 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 0 1 0 1)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  562    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  411    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  384    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  402    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra  652    permutation [ 3, 1, 2, 8, 6, 4, 5, 7 ]
vertex  8 -> Algebra  671    permutation [ 3, 1, 2, 8, 6, 4, 5, 7 ]

Algebra 411

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 7 ] 
[ 2, 7, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 1 1 0 0 0 1 1)
(0 1 1 0 0 0 1 1)
(0 1 1 1 0 1 0 1)
(0 0 0 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  568    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  261    permutation [ 3, 1, 2, 8, 4, 6, 5, 7 ]
vertex  6 -> Algebra  405    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  260    permutation [ 3, 1, 2, 8, 4, 6, 5, 7 ]
vertex  8 -> Algebra  270    permutation [ 3, 1, 2, 8, 4, 6, 5, 7 ]

Algebra 433

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 3, 8, 4, 2 ] 
[ 8, 4, 2, 3 ] 
[ 4, 2, 3, 8 ] 
[ 2, 1, 4 ] - [ 2, 3, 8, 4 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 1 1 1 0 1)
(0 1 1 1 1 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  3 -> Algebra  305    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  948    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  523    permutation [ 1, 4, 2, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  154    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  362    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 436

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 5, 4, 1 ] 
[ 3, 8, 2 ] 
[ 4, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 5, 4 ] 
[ 5, 4, 8 ] 
[ 8, 2, 4 ] - [ 8, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 
[ 2, 3, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 1 1 1 1 1 1)
(0 0 1 0 1 1 1 1)
(1 0 0 1 1 1 1 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  437    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  4 -> Algebra  154    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  948    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  850    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 437

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 4, 8, 5, 2 ] 
[ 8, 5, 2, 4 ] 
[ 5, 2, 4, 8 ] 
[ 2, 1, 5 ] - [ 2, 4, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 1 1 1 1)
(0 0 0 1 1 1 1 1)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra  399    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  436    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  955    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  949    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  815    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 446

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 3, 8, 4, 2 ] 
[ 8, 4, 2, 3 ] 
[ 2, 3, 8, 4 ] 
[ 4, 2, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  602    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  526    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  456    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  5 -> Algebra  361    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  7 -> Algebra  841    permutation [ 1, 2, 8, 3, 5, 7, 6, 4 ]

Algebra 456

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 3, 8, 5 ] 
[ 2, 3, 8 ] 
[ 5, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 5, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  612    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  556    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  476    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  971    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  970    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  446    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 476

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 3, 4, 8, 2 ] 
[ 4, 8, 2, 3 ] 
[ 4, 8, 5 ] 
[ 2, 3, 4, 8 ] 
[ 5, 4, 8 ] 
[ 8, 2, 3, 4 ] - [ 8, 5, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  632    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  592    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  456    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  840    permutation [ 1, 2, 4, 8, 5, 7, 6, 3 ]

Algebra 488

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 1 1 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  779    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  523    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  181    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  305    permutation [ 1, 3, 4, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra  731    permutation [ 1, 3, 4, 2, 5, 7, 6, 8 ]
vertex  8 -> Algebra  671    permutation [ 1, 3, 8, 2, 5, 6, 7, 4 ]

Algebra 490

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 1 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  781    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  184    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  525    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  731    permutation [ 1, 3, 4, 2, 5, 7, 6, 8 ]
vertex  6 -> Algebra  992    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  181    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  993    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 491

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 1, 2, 8, 4 ] 
[ 4, 1, 2, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 1 0 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  501    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  994    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  671    permutation [ 1, 3, 8, 2, 5, 6, 7, 4 ]
vertex  7 -> Algebra  993    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  181    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 497

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(1 1 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  338    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  990    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  532    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  499    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1005    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 499

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 2 ] 
[ 8, 3, 4, 2 ] 
[ 4, 2, 8, 3 ] 
[ 4, 2, 5 ] 
[ 3, 4, 2, 8 ] 
[ 2, 5, 4 ] - [ 2, 8, 3, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(1 1 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  340    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  992    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  534    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  184    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  497    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1009    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 500

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 1 0 0)
(1 1 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  893    permutation [ 3, 2, 8, 7, 6, 1, 4, 5 ]
vertex  3 -> Algebra 1010    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1009    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  185    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  184    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 501

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 4, 1, 2 ] 
[ 1, 2, 4 ] 
[ 2, 8, 5 ] 
[ 1, 2, 8 ] 
[ 5, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 5, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 1 0 0 0 1)
(1 1 1 1 0 0 0 1)
(1 0 0 1 0 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  404    permutation [ 3, 2, 8, 6, 7, 1, 4, 5 ]
vertex  2 -> Algebra  185    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1011    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  522    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  402    permutation [ 3, 2, 8, 6, 7, 1, 4, 5 ]
vertex  7 -> Algebra  893    permutation [ 3, 2, 8, 7, 6, 1, 4, 5 ]
vertex  8 -> Algebra  491    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 502

Quiver

[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 3, 2 ] 
[ 2, 5, 4, 3 ] 
[ 3, 2, 5, 4 ] 
[ 4, 3, 2, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 1 1 1 1 0)
(1 1 1 0 1 1 1 0)
(1 1 1 1 0 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  343    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1012    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  185    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1001    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1010    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  200    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 517

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  358    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1036    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1005    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1035    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  520    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 520

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  361    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1038    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1009    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  602    permutation [ 2, 1, 4, 8, 5, 6, 7, 3 ]
vertex  6 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  517    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 521

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 2, 8, 1 ] 
[ 8, 4, 3 ] 
[ 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  846    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  590    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1039    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1038    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  195    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 522

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 5 ] 
[ 1, 2, 4, 8 ] 
[ 5, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 5, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  848    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  501    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1040    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  195    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1039    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 523

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 1 ], [ 3, 4 ], [ 4, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 1 1 1 0 0 0)
(1 1 1 1 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra  527    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra  488    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  196    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  433    permutation [ 1, 3, 4, 2, 5, 6, 7, 8 ]
vertex  7 -> Algebra  941    permutation [ 1, 3, 4, 2, 5, 7, 6, 8 ]
vertex  8 -> Algebra  845    permutation [ 1, 3, 8, 2, 5, 6, 7, 4 ]

Algebra 525

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 0 0)
(1 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  490    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  941    permutation [ 1, 3, 4, 2, 5, 7, 6, 8 ]
vertex  6 -> Algebra 1043    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  196    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1044    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 526

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 3, 1 ] 
[ 8, 4, 2 ] 
[ 1, 2, 3 ] 
[ 4, 2, 3 ] 
[ 4, 2, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 1 1 0 0 0 1)
(1 1 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  855    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  536    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  446    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  994    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  845    permutation [ 1, 3, 8, 2, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1044    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  196    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 527

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 1 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 5, 1 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 5 ] 
[ 2, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 0)
(1 1 1 1 1 0 0 1)
(0 1 0 1 0 0 0 1)
(1 1 0 0 1 0 0 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra  197    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  537    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  523    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra  948    permutation [ 1, 3, 4, 5, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1045    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1046    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 529

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 8, 3, 5, 2 ] 
[ 4, 8, 3 ] 
[ 5, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 5, 2, 6 ] 
[ 2, 6, 5 ] - [ 2, 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 1)
(1 1 0 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  372    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1045    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  539    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  197    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1051    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 530

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 3, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 6, 5, 2 ] 
[ 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 1 0)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra  373    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1052    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1053    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1001    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  200    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1051    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  197    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 532

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 0 1)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 1 1 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  375    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1041    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  497    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  534    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1057    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 534

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 8 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 5 ] 
[ 2, 5, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 0 1)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  377    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1043    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  499    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  532    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1060    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 535

Quiver

[ 2, 1 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 0 0)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  378    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1061    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1010    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1051    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1060    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  200    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 536

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 1 ] 
[ 8, 5, 3 ] 
[ 2, 8, 5 ] 
[ 3, 8, 5 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 5, 2 ] 
[ 5, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  885    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  200    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  556    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1012    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1062    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1061    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  526    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 537

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 2, 3, 5, 8 ] 
[ 3, 1, 2 ] - [ 3, 5, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 1 0 0 0)
(1 1 1 0 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  201    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  558    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  527    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra  949    permutation [ 1, 3, 4, 5, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1063    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1064    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 538

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 6, 2 ] 
[ 5, 8, 3 ] 
[ 6, 2, 8, 3 ] 
[ 8, 3, 5 ] 
[ 6, 2, 7 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 6 ] 
[ 3, 5, 8 ] - [ 3, 6, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 1 1)
(1 1 1 0 1 1 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(1 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  381    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1065    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  541    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra  559    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  201    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1067    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 539

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 5, 8, 3 ] 
[ 8, 3, 5 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 0 1)
(1 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 1 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  382    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1063    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  560    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  529    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  201    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1069    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 540

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 6, 3, 8, 2 ] 
[ 8, 2, 6, 3 ] 
[ 3, 8, 2, 6 ] 
[ 2, 6, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 1 0)
(1 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  383    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1070    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  561    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1053    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1067    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1069    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  201    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 541

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 2 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 2 ] 
[ 8, 3, 2 ] 
[ 6, 8, 3 ] 
[ 8, 3, 6 ] 
[ 3, 2, 7 ] 
[ 2, 7, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 1 1)
(1 1 1 0 0 1 0 1)
(0 0 0 1 1 1 0 1)
(0 0 0 0 1 1 0 1)
(0 0 0 0 0 1 0 1)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  384    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1071    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  562    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  538    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra  757    permutation [ 3, 2, 1, 8, 6, 4, 5, 7 ]
vertex  8 -> Algebra  774    permutation [ 3, 2, 1, 8, 6, 4, 5, 7 ]

Algebra 556

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 5, 2, 3 ] 
[ 2, 3, 8, 5 ] 
[ 5, 2, 3, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 5, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra  456    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  593    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1087    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1085    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  536    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 558

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 1 0 0 0)
(1 1 1 1 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  211    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  537    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  909    permutation [ 1, 3, 4, 5, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1090    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1091    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 559

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ], [ 4, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 7, 6, 2 ] 
[ 8, 3, 6, 2 ] 
[ 4, 8, 3 ] 
[ 6, 2, 8, 3 ] 
[ 8, 3, 4 ] 
[ 6, 2, 7 ] 
[ 2, 7, 6 ] - [ 2, 8, 3, 6 ] 
[ 3, 4, 8 ] - [ 3, 6, 2, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 1 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra  402    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1092    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  562    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  5 -> Algebra  538    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  211    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1011    permutation [ 6, 2, 1, 7, 8, 4, 5, 3 ]

Algebra 560

Quiver

[ 2, 1 ], [ 2, 6 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 6 ] 
[ 2, 6, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  403    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1090    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  539    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  211    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1095    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 561

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 6, 3, 8, 2 ] 
[ 8, 2, 6, 3 ] 
[ 3, 8, 2, 6 ] 
[ 2, 6, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 1 0)
(1 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  404    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1096    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  540    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1011    permutation [ 6, 2, 1, 7, 8, 4, 5, 3 ]
vertex  7 -> Algebra 1095    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  211    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 562

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 2 ], [ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 6, 8 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 2 ] 
[ 8, 3, 2 ] 
[ 6, 8, 3 ] 
[ 8, 3, 6 ] 
[ 3, 2, 7 ] 
[ 2, 7, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 1 1)
(1 1 1 0 0 1 0 1)
(0 0 0 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 0 1 0 1)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  405    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1097    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  568    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  541    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  559    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra  758    permutation [ 3, 2, 1, 8, 6, 4, 5, 7 ]
vertex  8 -> Algebra  777    permutation [ 3, 2, 1, 8, 6, 4, 5, 7 ]

Algebra 568

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 2 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 7, 3, 2 ] 
[ 8, 3, 2 ] 
[ 4, 8, 3 ] 
[ 8, 3, 4 ] 
[ 3, 2, 7 ] 
[ 2, 7, 3 ] - [ 2, 8, 3 ] 
[ 3, 2, 8 ] - [ 3, 4, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 1 1)
(1 1 1 1 0 1 0 1)
(0 0 0 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 1 1 0)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra  411    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1105    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  317    permutation [ 3, 2, 1, 8, 4, 6, 5, 7 ]
vertex  6 -> Algebra  562    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  316    permutation [ 3, 2, 1, 8, 4, 6, 5, 7 ]
vertex  8 -> Algebra  326    permutation [ 3, 2, 1, 8, 4, 6, 5, 7 ]

Algebra 590

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 4, 2, 3 ] 
[ 2, 3, 8, 4 ] 
[ 4, 2, 3, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 4, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 0 1)
(1 1 1 1 1 1 0 1)
(0 1 1 1 1 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  4 -> Algebra 1124    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  673    permutation [ 4, 1, 2, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  230    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  521    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 592

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 3, 8 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 2, 3, 1 ] 
[ 4, 8, 2 ] 
[ 1, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 8, 5 ] 
[ 5, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 5, 4 ] 
[ 2, 3, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  593    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  476    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  230    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1124    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1040    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 593

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 2, 4, 1 ] 
[ 1, 2, 4 ] 
[ 8, 5, 2, 4 ] 
[ 2, 4, 8, 5 ] 
[ 5, 2, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 5, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 1 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  3 -> Algebra  556    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  592    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1128    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1125    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1012    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 602

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 8 ], [ 4, 1 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 3, 8, 4, 1 ] 
[ 8, 4, 1, 3 ] 
[ 1, 3, 8, 4 ] 
[ 4, 1, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 0 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(1 1 1 1 0 0 0 0)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  676    permutation [ 3, 2, 1, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  446    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  612    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  5 -> Algebra  520    permutation [ 2, 1, 8, 3, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1035    permutation [ 2, 1, 8, 3, 5, 7, 6, 4 ]

Algebra 612

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 1 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 4, 1, 3 ] 
[ 1, 3, 4 ] 
[ 3, 8, 5 ] 
[ 1, 3, 8 ] 
[ 5, 3, 8 ] 
[ 3, 4, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 5, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  456    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  632    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1144    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1143    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  602    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 632

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 3, 4, 8, 1 ] 
[ 4, 8, 1, 3 ] 
[ 4, 8, 5 ] 
[ 1, 3, 4, 8 ] 
[ 5, 4, 8 ] 
[ 8, 1, 3, 4 ] - [ 8, 5, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 0 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  476    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  612    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1034    permutation [ 2, 1, 4, 8, 5, 7, 6, 3 ]

Algebra 647

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 5, 8, 1 ] 
[ 4, 5, 8, 3 ] 
[ 5, 8, 3, 4 ] 
[ 1, 5, 8 ] 
[ 3, 4, 5, 8 ] 
[ 8, 1, 5 ] - [ 8, 3, 4, 5 ] 

Cartan matrix

(1 0 0 0 1 0 0 0)
(0 1 1 1 1 0 0 0)
(0 0 1 1 1 0 0 0)
(0 0 0 1 1 0 0 1)
(0 0 1 0 1 0 0 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  753    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  677    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  654    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  840    permutation [ 2, 3, 5, 8, 1, 7, 6, 4 ]
vertex  7 -> Algebra  829    permutation [ 2, 3, 5, 8, 7, 6, 1, 4 ]

Algebra 651

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 4, 1, 8, 3 ] 
[ 4, 1, 5 ] 
[ 3, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 1 0 0 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  757    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  652    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  384    permutation [ 2, 3, 1, 6, 7, 5, 8, 4 ]

Algebra 652

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 4, 1 ] 
[ 8, 3, 4, 1 ] 
[ 4, 1, 8, 3 ] 
[ 4, 1, 5 ] 
[ 3, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 3, 4 ] 

Cartan matrix

(1 0 1 1 1 0 0 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  758    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  260    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  651    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  405    permutation [ 2, 3, 1, 6, 7, 5, 8, 4 ]

Algebra 654

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 4, 8, 1 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  760    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  706    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  647    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  970    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1164    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  838    permutation [ 2, 3, 4, 8, 6, 7, 1, 5 ]

Algebra 668

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ]

Relations

[ 4, 3, 8, 1 ] 
[ 8, 1, 4, 3 ] 
[ 3, 8, 1, 4 ] 
[ 1, 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  774    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  731    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  384    permutation [ 2, 3, 1, 6, 7, 5, 8, 4 ]
vertex  5 -> Algebra  993    permutation [ 1, 4, 2, 8, 5, 7, 6, 3 ]
vertex  6 -> Algebra  671    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 671

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 4, 3, 8, 1 ] 
[ 8, 1, 4, 3 ] 
[ 3, 8, 1, 4 ] 
[ 1, 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  777    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  488    permutation [ 1, 4, 2, 8, 5, 6, 7, 3 ]
vertex  4 -> Algebra  405    permutation [ 2, 3, 1, 6, 7, 5, 8, 4 ]
vertex  5 -> Algebra  491    permutation [ 1, 4, 2, 8, 5, 6, 7, 3 ]
vertex  6 -> Algebra  270    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  668    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 673

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  677    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  5 -> Algebra  272    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  590    permutation [ 2, 3, 4, 1, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1119    permutation [ 2, 3, 4, 1, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1038    permutation [ 2, 3, 8, 1, 5, 6, 7, 4 ]

Algebra 675

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(1 1 1 1 0 0 0 1)
(1 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  5 -> Algebra 1119    permutation [ 2, 3, 4, 1, 5, 7, 6, 8 ]
vertex  6 -> Algebra 1180    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  272    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1181    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 676

Quiver

[ 1, 3 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 2 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 3, 4, 1 ] 
[ 8, 4, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 4, 1, 8 ] 
[ 4, 1, 3 ] - [ 4, 2, 3 ] 
[ 1, 3, 4 ] - [ 1, 8, 4 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  855    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  602    permutation [ 3, 2, 1, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1038    permutation [ 2, 3, 8, 1, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1181    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  272    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 677

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 5, 8, 1 ] 
[ 3, 4, 2 ] 
[ 5, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 1, 5, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 1 0 0 1)

Good mutations

vertex  3 -> Algebra  687    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  647    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  673    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  6 -> Algebra 1124    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1182    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1183    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 687

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 3, 5, 8, 1 ] 
[ 3, 5, 2 ] 
[ 2, 3, 5 ] 
[ 8, 1, 3, 5 ] 
[ 1, 3, 5, 8 ] 
[ 5, 2, 3 ] - [ 5, 8, 1, 3 ] 

Cartan matrix

(1 0 1 0 1 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 0 1 0 0 1)
(1 1 1 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(1 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra  706    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  677    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra 1125    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1198    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 706

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra  654    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  687    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1085    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1221    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1222    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 731

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 1 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 4, 3, 1 ] 
[ 3, 8, 2 ] 
[ 1, 4, 3 ] 
[ 2, 3, 8 ] 
[ 4, 3, 8 ] 
[ 8, 2, 3 ] - [ 8, 4, 3 ] 
[ 3, 1, 4 ] - [ 3, 8, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 0)
(1 1 1 0 0 0 0 0)
(1 0 1 1 1 0 0 1)
(0 0 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1243    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  941    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  490    permutation [ 1, 4, 2, 3, 5, 7, 6, 8 ]
vertex  6 -> Algebra  488    permutation [ 1, 4, 2, 3, 5, 7, 6, 8 ]
vertex  8 -> Algebra  668    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 734

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 3, 8, 4, 1 ] 
[ 3, 8, 2 ] 
[ 1, 3, 8, 4 ] 
[ 2, 3, 8 ] 
[ 4, 1, 3, 8 ] 
[ 8, 2, 3 ] - [ 8, 4, 1, 3 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 1 1 0 1)
(1 0 1 1 1 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  305    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  779    permutation [ 4, 1, 2, 3, 5, 6, 7, 8 ]
vertex  7 -> Algebra  306    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 753

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 5, 8, 1 ] 
[ 4, 5, 8, 2 ] 
[ 5, 8, 2, 4 ] 
[ 1, 5, 8 ] 
[ 2, 4, 5, 8 ] 
[ 8, 1, 5 ] - [ 8, 2, 4, 5 ] 

Cartan matrix

(1 0 0 0 1 0 0 0)
(0 1 1 1 1 0 0 0)
(0 0 1 0 0 0 0 0)
(0 0 0 1 1 0 0 1)
(0 1 1 0 1 0 0 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  3 -> Algebra  647    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  760    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1034    permutation [ 3, 2, 5, 8, 1, 7, 6, 4 ]
vertex  7 -> Algebra 1024    permutation [ 3, 2, 5, 8, 7, 6, 1, 4 ]

Algebra 757

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 5, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 4, 1, 8, 2 ] 
[ 4, 1, 5 ] 
[ 2, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  787    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  651    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  758    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  541    permutation [ 3, 2, 1, 6, 7, 5, 8, 4 ]

Algebra 758

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 4, 1 ] 
[ 8, 2, 4, 1 ] 
[ 4, 1, 8, 2 ] 
[ 4, 1, 5 ] 
[ 2, 4, 1, 8 ] 
[ 1, 5, 4 ] - [ 1, 8, 2, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  789    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  652    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  316    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  757    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  562    permutation [ 3, 2, 1, 6, 7, 5, 8, 4 ]

Algebra 759

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 1 ], [ 3, 2 ], [ 4, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 3, 2, 1 ] 
[ 5, 4, 2, 1 ] 
[ 2, 1, 3 ] 
[ 2, 1, 5, 4 ] 
[ 4, 2, 1, 5 ] 
[ 1, 3, 2 ] - [ 1, 5, 4, 2 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 0 0 1 1 1 0)
(0 1 1 0 0 0 0 0)
(1 1 0 1 0 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  317    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  364    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1105    permutation [ 3, 2, 1, 5, 7, 6, 8, 4 ]
vertex  8 -> Algebra  332    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]

Algebra 760

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 1 ], [ 6, 7 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 4, 8, 1 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 1, 4, 8 ] 
[ 2, 4, 8 ] 
[ 4, 5, 2 ] - [ 4, 8, 2 ] 
[ 8, 1, 4 ] - [ 8, 2, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 0)
(1 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  3 -> Algebra  654    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  753    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1143    permutation [ 2, 3, 4, 5, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1254    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1032    permutation [ 3, 2, 4, 8, 6, 7, 1, 5 ]

Algebra 774

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ]

Relations

[ 4, 2, 8, 1 ] 
[ 8, 1, 4, 2 ] 
[ 2, 8, 1, 4 ] 
[ 1, 4, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  842    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  668    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  541    permutation [ 3, 2, 1, 6, 7, 5, 8, 4 ]
vertex  5 -> Algebra 1269    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  777    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 777

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 4, 2, 8, 1 ] 
[ 8, 1, 4, 2 ] 
[ 2, 8, 1, 4 ] 
[ 1, 4, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  845    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  671    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  562    permutation [ 3, 2, 1, 6, 7, 5, 8, 4 ]
vertex  5 -> Algebra  994    permutation [ 1, 4, 3, 8, 5, 6, 7, 2 ]
vertex  6 -> Algebra  326    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  774    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 779

Quiver

[ 1, 2 ], [ 1, 5 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 1 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra  488    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  328    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  734    permutation [ 2, 3, 4, 1, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1243    permutation [ 2, 3, 4, 1, 5, 7, 6, 8 ]

Algebra 781

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(1 1 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  331    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  490    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1243    permutation [ 2, 3, 4, 1, 5, 7, 6, 8 ]
vertex  6 -> Algebra 1271    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  328    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 787

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 4, 8, 3 ] 
[ 2, 1, 5 ] 
[ 3, 4, 8 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(1 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 1 0 1 1 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1270    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  338    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  757    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra  789    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  956    permutation [ 3, 1, 6, 7, 5, 8, 4, 2 ]

Algebra 789

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 5, 2, 1 ] 
[ 8, 2, 1 ] 
[ 4, 8, 2 ] 
[ 4, 8, 3 ] 
[ 2, 1, 5 ] 
[ 3, 4, 8 ] 
[ 1, 5, 2 ] - [ 1, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 
[ 2, 1, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(1 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 0 0 1 0 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1271    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  340    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  758    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra  331    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  787    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  913    permutation [ 3, 1, 6, 7, 5, 8, 4, 2 ]

Algebra 790

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 3, 8, 1 ] 
[ 5, 2, 8, 1 ] 
[ 8, 1, 5, 2 ] 
[ 8, 1, 3 ] 
[ 2, 8, 1, 5 ] 
[ 1, 3, 8 ] - [ 1, 5, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 1 0 1)
(1 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra  811    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  4 -> Algebra 1105    permutation [ 3, 8, 1, 5, 7, 6, 4, 2 ]
vertex  6 -> Algebra  913    permutation [ 3, 1, 6, 7, 5, 8, 4, 2 ]
vertex  7 -> Algebra  332    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  331    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 802

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 2, 4, 3 ] 
[ 3, 2, 4 ] 
[ 5, 2, 4 ] 
[ 5, 2, 6 ] 
[ 4, 3, 2 ] - [ 4, 5, 2 ] 
[ 2, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 1 0 1 1 1 1 0)
(0 1 0 1 1 1 1 0)
(0 1 1 0 0 1 1 0)
(0 1 1 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1001    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1294    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  958    permutation [ 1, 2, 8, 3, 4, 6, 7, 5 ]
vertex  5 -> Algebra  343    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1291    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  373    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 806

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 1 0 0 0)
(0 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(0 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1005    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1297    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1298    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  358    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1165    permutation [ 7, 1, 2, 3, 8, 4, 6, 5 ]
vertex  6 -> Algebra  810    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  338    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 810

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(0 1 1 1 1 0 0 0)
(0 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1009    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1302    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  959    permutation [ 1, 2, 5, 8, 3, 6, 7, 4 ]
vertex  4 -> Algebra  361    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  971    permutation [ 1, 2, 3, 8, 4, 6, 7, 5 ]
vertex  6 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  806    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  340    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 811

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 3, 2, 1 ] 
[ 5, 2, 1 ] 
[ 8, 5, 2 ] 
[ 2, 1, 3 ] 
[ 5, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 5, 2 ] 
[ 2, 1, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 1 1 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  383    permutation [ 3, 1, 8, 7, 6, 2, 4, 5 ]
vertex  2 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1303    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  847    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1302    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  342    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  790    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 812

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 4, 3, 2 ] 
[ 2, 5, 4, 3 ] 
[ 3, 2, 5, 4 ] 
[ 4, 3, 2, 5 ] 

Cartan matrix

(1 1 0 1 1 1 0 0)
(0 1 0 1 1 1 0 0)
(0 1 1 0 1 1 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1010    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1304    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1291    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  959    permutation [ 1, 2, 5, 8, 3, 6, 7, 4 ]
vertex  7 -> Algebra  343    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  378    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 813

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 3, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 5, 2, 3, 1 ] 
[ 3, 1, 5, 2 ] 
[ 8, 5, 2 ] 
[ 1, 5, 2, 3 ] 
[ 5, 2, 8 ] 
[ 2, 3, 1, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 0 1 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 0 1 0 1 1 1 0)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1096    permutation [ 1, 3, 8, 6, 7, 2, 4, 5 ]
vertex  2 -> Algebra  815    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  342    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  850    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1305    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1303    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 815

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 3, 5, 2 ] 
[ 3, 5, 4 ] 
[ 4, 3, 5 ] 
[ 5, 2, 3 ] - [ 5, 4, 3 ] 
[ 2, 1, 5 ] - [ 2, 3, 5 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 0 1 1 1 0)
(0 0 1 0 1 1 1 0)
(0 0 1 1 0 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1307    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  343    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  813    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  437    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1308    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1304    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  379    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 829

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 2 ] 
[ 2, 8, 3, 4 ] 
[ 7, 3, 4 ] 
[ 3, 4, 7 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 7, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 1 1 1 0 0 1 1)
(0 0 1 0 1 1 1 0)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1024    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1182    permutation [ 7, 1, 8, 2, 3, 6, 5, 4 ]
vertex  5 -> Algebra  647    permutation [ 7, 1, 2, 8, 3, 6, 5, 4 ]
vertex  8 -> Algebra 1164    permutation [ 7, 1, 2, 3, 8, 6, 5, 4 ]

Algebra 830

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 0)
(0 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 1 1 0 1 1 1)
(0 0 1 1 0 0 1 1)
(0 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1025    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1327    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1164    permutation [ 7, 1, 2, 3, 8, 6, 5, 4 ]
vertex  5 -> Algebra  838    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 838

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 0)
(0 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 0 1 1)
(0 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1032    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1337    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  654    permutation [ 7, 1, 2, 3, 8, 5, 6, 4 ]
vertex  5 -> Algebra  841    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra  830    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 840

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 7 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 2 ] 
[ 2, 8, 3, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 1 1 1 1 0 1 1)
(0 0 1 0 1 0 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1034    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1124    permutation [ 1, 8, 2, 3, 5, 7, 6, 4 ]
vertex  6 -> Algebra  476    permutation [ 1, 2, 8, 3, 5, 7, 6, 4 ]
vertex  7 -> Algebra  647    permutation [ 5, 1, 2, 8, 3, 7, 6, 4 ]
vertex  8 -> Algebra  970    permutation [ 1, 2, 3, 8, 5, 7, 6, 4 ]

Algebra 841

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 0)
(0 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 0 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1035    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1044    permutation [ 1, 4, 2, 8, 5, 7, 6, 3 ]
vertex  4 -> Algebra  970    permutation [ 1, 2, 3, 8, 5, 7, 6, 4 ]
vertex  5 -> Algebra  358    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  446    permutation [ 1, 2, 4, 8, 5, 7, 6, 3 ]
vertex  7 -> Algebra  838    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]

Algebra 842

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 8, 4, 2 ] 
[ 8, 4, 3 ] 
[ 3, 8, 4 ] 
[ 2, 1, 4 ] - [ 2, 8, 4 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(0 0 1 0 0 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1340    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  358    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  941    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1341    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1044    permutation [ 1, 4, 2, 8, 5, 7, 6, 3 ]
vertex  6 -> Algebra  845    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  774    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 845

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 8, 4, 2 ] 
[ 8, 4, 3 ] 
[ 3, 8, 4 ] 
[ 2, 1, 4 ] - [ 2, 8, 4 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(0 0 1 0 0 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1345    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  361    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  523    permutation [ 1, 4, 2, 8, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1346    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  526    permutation [ 1, 4, 2, 8, 5, 6, 7, 3 ]
vertex  6 -> Algebra  362    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  842    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  777    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 846

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 8, 4, 3 ] 
[ 1, 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 4, 1, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 1 1 1 0 1)
(0 0 1 0 0 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  362    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  521    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1347    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1345    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  363    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 847

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 3, 4, 1 ] 
[ 5, 4, 1 ] 
[ 4, 1, 3 ] 
[ 8, 5, 4 ] 
[ 5, 4, 8 ] 
[ 1, 3, 4 ] - [ 1, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 1 1 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 0 1 1 0 0 0 1)
(1 0 0 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  895    permutation [ 3, 1, 8, 7, 6, 4, 2, 5 ]
vertex  2 -> Algebra  811    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1348    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  362    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1346    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  364    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1105    permutation [ 3, 4, 1, 5, 7, 6, 2, 8 ]

Algebra 848

Quiver

[ 1, 2 ], [ 1, 4 ], [ 2, 8 ], [ 3, 4 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 2, 8, 1 ] 
[ 4, 8, 1 ] 
[ 8, 1, 2 ] 
[ 4, 8, 5 ] 
[ 5, 4, 8 ] 
[ 8, 1, 4 ] - [ 8, 5, 4 ] 
[ 1, 2, 8 ] - [ 1, 4, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 0 0 1 1 1 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  849    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  2 -> Algebra  522    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1350    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  363    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1347    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 849

Quiver

[ 1, 4 ], [ 2, 4 ], [ 3, 1 ], [ 4, 8 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 4, 8, 5, 1 ] 
[ 8, 5, 1, 4 ] 
[ 1, 4, 8, 5 ] 
[ 5, 1, 4, 8 ] 

Cartan matrix

(1 0 0 1 0 0 0 1)
(0 1 0 1 1 1 1 1)
(1 0 1 1 0 0 0 1)
(0 0 0 1 1 1 1 1)
(1 0 0 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  364    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  404    permutation [ 3, 1, 8, 6, 7, 4, 2, 5 ]
vertex  3 -> Algebra 1095    permutation [ 3, 1, 8, 6, 7, 4, 2, 5 ]
vertex  4 -> Algebra  848    permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex  5 -> Algebra  403    permutation [ 3, 1, 8, 6, 7, 4, 2, 5 ]
vertex  7 -> Algebra  895    permutation [ 3, 1, 8, 7, 6, 4, 2, 5 ]

Algebra 850

Quiver

[ 1, 5 ], [ 2, 4 ], [ 3, 1 ], [ 4, 3 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 5, 4, 3, 1 ] 
[ 1, 5, 4, 3 ] 
[ 3, 1, 5, 4 ] 
[ 8, 5, 4 ] 
[ 5, 4, 8 ] 
[ 4, 3, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 0 1 0 1 1 1 0)
(1 0 1 1 1 1 1 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1351    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  813    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  364    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  436    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1352    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1348    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 855

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 1 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 3, 4, 1 ] 
[ 8, 4, 1 ] 
[ 3, 4, 1, 2 ] 
[ 4, 1, 2, 3 ] 
[ 4, 1, 8 ] 
[ 1, 2, 3, 4 ] - [ 1, 8, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 0)
(1 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  865    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]
vertex  2 -> Algebra  526    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  676    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1345    permutation [ 2, 3, 8, 1, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1359    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 865

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 8, 5, 1 ] 
[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 1, 8, 5 ] 
[ 2, 8, 5 ] 
[ 4, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 5, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 
[ 5, 1, 8 ] - [ 5, 2, 8 ] 

Cartan matrix

(1 0 0 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(1 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra  885    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  4 -> Algebra 1103    permutation [ 1, 8, 5, 6, 7, 4, 3, 2 ]
vertex  5 -> Algebra 1379    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1378    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  855    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]

Algebra 874

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 3, 8 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 6, 5, 2 ] 
[ 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 1 1 0 1 1 0 0)
(0 1 1 0 1 1 0 0)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 0 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1051    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1395    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1396    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1291    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  378    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1379    permutation [ 1, 6, 7, 5, 2, 8, 4, 3 ]
vertex  7 -> Algebra  373    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  372    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 875

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 6, 2 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 3, 2, 1 ] 
[ 6, 2, 1 ] 
[ 8, 6, 2 ] 
[ 2, 1, 3 ] 
[ 6, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 0 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1397    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  373    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1398    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1294    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  886    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1395    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 876

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 6, 5, 3, 2 ] 
[ 2, 6, 5, 3 ] 
[ 3, 2, 6, 5 ] 
[ 5, 3, 2, 6 ] 

Cartan matrix

(1 1 0 0 1 1 1 0)
(0 1 0 0 1 1 1 0)
(0 1 1 0 0 1 1 0)
(0 0 0 1 0 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1053    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1302    permutation [ 2, 6, 1, 7, 3, 8, 4, 5 ]
vertex  3 -> Algebra  373    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  958    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1393    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1396    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  383    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 880

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 1 1 1 0 1 1)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1057    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1402    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1298    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1174    permutation [ 7, 1, 2, 3, 8, 4, 6, 5 ]
vertex  6 -> Algebra  883    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  375    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 883

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1060    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1091    permutation [ 1, 5, 2, 8, 4, 6, 7, 3 ]
vertex  4 -> Algebra  959    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]
vertex  5 -> Algebra  976    permutation [ 1, 2, 3, 8, 4, 6, 7, 5 ]
vertex  6 -> Algebra  378    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  880    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  377    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 884

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 8, 5, 2 ] 
[ 8, 5, 3 ] 
[ 3, 8, 5 ] 
[ 2, 1, 5 ] - [ 2, 8, 5 ] 
[ 5, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 0 1 0 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1405    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  378    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  909    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1304    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1406    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1091    permutation [ 1, 5, 2, 8, 4, 6, 7, 3 ]
vertex  7 -> Algebra  379    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 885

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 5, 1 ], [ 5, 3 ], [ 5, 6 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 5, 1 ] 
[ 8, 5, 1, 2 ] 
[ 8, 5, 3 ] 
[ 1, 2, 8, 5 ] 
[ 3, 8, 5 ] 
[ 5, 1, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 0 1 1 1 1 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  379    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  536    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1307    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1395    permutation [ 1, 8, 2, 7, 4, 5, 3, 6 ]
vertex  7 -> Algebra 1405    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  865    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 886

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 5 ], [ 3, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 3, 5, 1 ] 
[ 6, 5, 1 ] 
[ 5, 1, 3 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 1, 3, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 1 0 1 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 1 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1407    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  875    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1408    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1308    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  379    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1406    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 893

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 7, 6, 2 ] 
[ 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 6, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 1 1 0 0 1 1 0)
(0 1 1 0 0 1 1 0)
(0 1 1 0 1 1 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 0 1 1)

Good mutations

vertex  1 -> Algebra 1067    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  500    permutation [ 6, 2, 1, 7, 8, 5, 4, 3 ]
vertex  3 -> Algebra  993    permutation [ 6, 3, 1, 7, 8, 5, 4, 2 ]
vertex  4 -> Algebra  501    permutation [ 6, 2, 1, 7, 8, 5, 4, 3 ]
vertex  5 -> Algebra 1393    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra  383    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1039    permutation [ 6, 7, 1, 2, 8, 5, 4, 3 ]
vertex  8 -> Algebra  381    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 895

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 3 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 6, 3, 8, 2 ] 
[ 8, 2, 6, 3 ] 
[ 3, 8, 2, 6 ] 
[ 2, 6, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 1 0 0)
(0 1 1 0 0 1 0 0)
(0 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 0 1 1 0 1)
(0 0 1 0 1 1 1 1)
(0 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1069    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  847    permutation [ 2, 7, 1, 6, 8, 5, 4, 3 ]
vertex  4 -> Algebra  849    permutation [ 2, 7, 1, 6, 8, 5, 4, 3 ]
vertex  5 -> Algebra 1396    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1347    permutation [ 6, 7, 1, 2, 8, 5, 4, 3 ]
vertex  7 -> Algebra  383    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  382    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 909

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 3, 8, 5, 2 ] 
[ 8, 5, 2, 3 ] 
[ 5, 2, 3, 8 ] 
[ 2, 1, 5 ] - [ 2, 3, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 0 1)

Good mutations

vertex  4 -> Algebra  949    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1092    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  558    permutation [ 1, 5, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  399    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  884    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 912

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 3, 8, 2 ] 
[ 5, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 6, 5 ] 
[ 6, 5, 8 ] 
[ 8, 2, 5 ] - [ 8, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 
[ 2, 3, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 1 1 1 1 1 1)
(0 0 1 1 0 1 1 1)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  913    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  4 -> Algebra  955    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  399    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1092    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1408    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 913

Quiver

[ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 6, 2, 1 ] 
[ 1, 6, 2 ] 
[ 5, 8, 6, 2 ] 
[ 8, 6, 2, 5 ] 
[ 6, 2, 5, 8 ] 
[ 2, 1, 6 ] - [ 2, 5, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 0 0 1 1 1 1)
(0 0 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 1 1 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra  790    permutation [ 2, 8, 1, 7, 5, 3, 4, 6 ]
vertex  4 -> Algebra  956    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  912    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra  789    permutation [ 2, 8, 1, 7, 5, 3, 4, 6 ]
vertex  7 -> Algebra 1097    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1302    permutation [ 2, 6, 1, 7, 5, 3, 4, 8 ]

Algebra 941

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 3, 8, 4, 2 ] 
[ 8, 4, 2, 3 ] 
[ 4, 2, 3, 8 ] 
[ 2, 1, 4 ] - [ 2, 3, 8, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  3 -> Algebra  731    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1045    permutation [ 1, 5, 2, 3, 4, 7, 6, 8 ]
vertex  5 -> Algebra  525    permutation [ 1, 4, 2, 3, 5, 7, 6, 8 ]
vertex  6 -> Algebra  523    permutation [ 1, 4, 2, 3, 5, 7, 6, 8 ]
vertex  8 -> Algebra  842    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 948

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 5, 4, 1 ] 
[ 3, 8, 2 ] 
[ 4, 8, 2 ] 
[ 8, 2, 3 ] 
[ 1, 5, 4 ] 
[ 5, 4, 8 ] 
[ 8, 2, 4 ] - [ 8, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 
[ 2, 3, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(1 1 1 1 1 1 0 1)
(0 0 1 0 1 1 0 1)
(1 0 0 1 1 1 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra  949    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  4 -> Algebra  433    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  527    permutation [ 1, 5, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  436    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1348    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 949

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 4, 8, 5, 2 ] 
[ 8, 5, 2, 4 ] 
[ 5, 2, 4, 8 ] 
[ 2, 1, 5 ] - [ 2, 4, 8, 5 ] 

Cartan matrix

(1 0 0 0 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 0 1 1 1 1 0 1)
(0 0 0 1 1 1 0 1)
(0 1 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 0 1)

Good mutations

vertex  3 -> Algebra  909    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra  948    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1065    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  537    permutation [ 1, 5, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  437    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1304    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 955

Quiver

[ 1, 6 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 4, 8, 2 ] 
[ 5, 8, 2 ] 
[ 8, 2, 4 ] 
[ 1, 6, 5 ] 
[ 6, 5, 8 ] 
[ 8, 2, 5 ] - [ 8, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 
[ 2, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 0 1 1 1 1 1)
(0 0 1 1 0 1 1 1)
(0 0 0 1 0 1 1 1)
(1 0 0 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  956    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  912    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  437    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1065    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1447    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 956

Quiver

[ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 6, 2, 1 ] 
[ 1, 6, 2 ] 
[ 5, 8, 6, 2 ] 
[ 8, 6, 2, 5 ] 
[ 6, 2, 5, 8 ] 
[ 2, 1, 6 ] - [ 2, 5, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 0)
(1 1 0 0 1 1 1 1)
(0 0 1 1 1 1 1 1)
(0 0 0 1 1 1 1 1)
(0 0 0 0 1 1 1 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra  913    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  955    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra  787    permutation [ 2, 8, 1, 7, 5, 3, 4, 6 ]
vertex  7 -> Algebra 1071    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1297    permutation [ 2, 6, 1, 7, 5, 3, 4, 8 ]

Algebra 958

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 7 ], [ 6, 8 ], [ 8, 5 ]

Relations

[ 6, 8, 5, 2 ] 
[ 2, 6, 8, 5 ] 
[ 8, 5, 2, 6 ] 
[ 5, 2, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 1 1 1)
(0 1 0 0 0 1 1 1)
(0 1 1 1 1 1 1 0)
(0 1 0 1 1 1 1 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1131    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1297    permutation [ 2, 6, 1, 7, 5, 3, 4, 8 ]
vertex  3 -> Algebra  876    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  5 -> Algebra  802    permutation [ 1, 2, 4, 5, 8, 6, 7, 3 ]
vertex  6 -> Algebra 1449    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1442    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 959

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 8, 5, 2 ] 
[ 8, 5, 2, 3 ] 
[ 2, 3, 8, 5 ] 
[ 5, 2, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 0 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1132    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1064    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  964    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra  883    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  5 -> Algebra  810    permutation [ 1, 2, 5, 8, 3, 6, 7, 4 ]
vertex  6 -> Algebra  812    permutation [ 1, 2, 5, 8, 3, 6, 7, 4 ]
vertex  7 -> Algebra 1298    permutation [ 1, 2, 5, 8, 3, 7, 6, 4 ]

Algebra 964

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 5, 2, 3 ] 
[ 2, 3, 5 ] 
[ 3, 8, 6 ] 
[ 2, 3, 8 ] 
[ 6, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 6, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1137    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1077    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  976    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  971    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra 1451    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1169    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  959    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 970

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 3, 8, 5 ] 
[ 2, 3, 8 ] 
[ 5, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 5, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1143    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1085    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  840    permutation [ 1, 2, 3, 8, 5, 7, 6, 4 ]
vertex  5 -> Algebra 1165    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  654    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  456    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  841    permutation [ 1, 2, 3, 8, 5, 7, 6, 4 ]

Algebra 971

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 4, 2, 3 ] 
[ 5, 8, 2, 3 ] 
[ 2, 3, 4 ] 
[ 5, 8, 6 ] 
[ 2, 3, 5, 8 ] 
[ 6, 5, 8 ] 
[ 3, 4, 2 ] - [ 3, 5, 8, 2 ] 
[ 8, 2, 3, 5 ] - [ 8, 6, 5 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(0 1 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1144    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1087    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  964    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  456    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1165    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  810    permutation [ 1, 2, 3, 5, 8, 6, 7, 4 ]

Algebra 976

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 4, 2, 3 ] 
[ 2, 3, 4 ] 
[ 3, 8, 6 ] 
[ 2, 3, 8 ] 
[ 6, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 6, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1149    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1103    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  964    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1379    permutation [ 1, 8, 7, 6, 2, 4, 5, 3 ]
vertex  7 -> Algebra 1174    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  883    permutation [ 1, 2, 3, 5, 8, 6, 7, 4 ]

Algebra 990

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 1 0 1 1 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1270    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  497    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1041    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  992    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1173    permutation [ 1, 3, 8, 2, 6, 7, 5, 4 ]

Algebra 992

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 4, 1 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4 ] 
[ 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 1 0 1 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1271    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  499    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1043    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  490    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  990    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1177    permutation [ 1, 3, 8, 2, 6, 7, 5, 4 ]

Algebra 993

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 1 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 1, 2, 8, 4 ] 
[ 4, 1, 2, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 1 0 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra  893    permutation [ 3, 8, 2, 7, 6, 1, 4, 5 ]
vertex  3 -> Algebra 1269    permutation [ 1, 8, 3, 2, 5, 7, 6, 4 ]
vertex  5 -> Algebra  668    permutation [ 1, 3, 8, 2, 5, 7, 6, 4 ]
vertex  6 -> Algebra 1177    permutation [ 1, 3, 8, 2, 6, 7, 5, 4 ]
vertex  7 -> Algebra  491    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  490    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 994

Quiver

[ 1, 2 ], [ 2, 8 ], [ 4, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 1, 2, 8, 4 ] 
[ 4, 1, 2, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 1 0 1 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1011    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  491    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  777    permutation [ 1, 8, 3, 2, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1269    permutation [ 1, 8, 3, 2, 5, 7, 6, 4 ]
vertex  8 -> Algebra  526    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1001

Quiver

[ 2, 1 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 2, 4, 3 ] 
[ 3, 2, 4 ] 
[ 5, 2, 4 ] 
[ 5, 2, 6 ] 
[ 4, 3, 2 ] - [ 4, 5, 2 ] 
[ 2, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 1 1 1 1 0)
(1 1 1 0 0 1 1 0)
(1 1 1 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra  802    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1456    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1131    permutation [ 1, 2, 8, 3, 4, 6, 7, 5 ]
vertex  5 -> Algebra  502    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1455    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  530    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1005

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 0)
(1 1 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(1 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  806    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1449    permutation [ 3, 2, 6, 7, 5, 1, 4, 8 ]
vertex  3 -> Algebra 1457    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  517    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1255    permutation [ 7, 2, 1, 3, 8, 4, 6, 5 ]
vertex  6 -> Algebra 1009    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  497    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1009

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 5, 4, 2 ] 
[ 4, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 2, 5 ] 
[ 2, 3, 8 ] 
[ 3, 4, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 4 ] - [ 2, 5, 4 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 1 0 0 0)
(1 1 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  810    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1393    permutation [ 3, 2, 5, 7, 8, 1, 4, 6 ]
vertex  3 -> Algebra 1132    permutation [ 2, 1, 5, 8, 3, 6, 7, 4 ]
vertex  4 -> Algebra  520    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1144    permutation [ 2, 1, 3, 8, 4, 6, 7, 5 ]
vertex  6 -> Algebra  500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1005    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  499    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1010

Quiver

[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 4, 3, 2 ] 
[ 2, 5, 4, 3 ] 
[ 3, 2, 5, 4 ] 
[ 4, 3, 2, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(1 1 1 1 0 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  812    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1460    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1455    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1132    permutation [ 2, 1, 5, 8, 3, 6, 7, 4 ]
vertex  7 -> Algebra  502    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  535    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1011

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 4, 1 ], [ 5, 2 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 4, 1, 2 ] 
[ 1, 2, 4 ] 
[ 2, 8, 5 ] 
[ 1, 2, 8 ] 
[ 5, 2, 8 ] 
[ 2, 4, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 5, 2 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(1 1 1 1 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 0 0 1 0 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  561    permutation [ 3, 2, 8, 6, 7, 1, 4, 5 ]
vertex  2 -> Algebra 1012    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  501    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1040    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  559    permutation [ 3, 2, 8, 6, 7, 1, 4, 5 ]
vertex  7 -> Algebra 1067    permutation [ 3, 2, 8, 7, 6, 1, 4, 5 ]
vertex  8 -> Algebra  994    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1012

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 3, 5, 4 ] 
[ 2, 3, 5 ] 
[ 4, 3, 5 ] 
[ 3, 1, 2 ] - [ 3, 5, 2 ] 
[ 5, 2, 3 ] - [ 5, 4, 3 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(1 1 1 0 1 1 1 0)
(1 0 1 1 0 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1307    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  502    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1011    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  593    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1461    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1460    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  536    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1024

Quiver

[ 2, 1 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 2 ] 
[ 2, 8, 3, 4 ] 
[ 7, 3, 4 ] 
[ 3, 4, 7 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 7, 3 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 0 1)
(1 1 1 1 0 0 0 0)
(1 1 1 1 0 0 1 1)
(0 0 1 0 1 1 1 0)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  829    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  753    permutation [ 7, 2, 1, 8, 3, 6, 5, 4 ]
vertex  8 -> Algebra 1254    permutation [ 7, 2, 1, 3, 8, 6, 5, 4 ]

Algebra 1025

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 1 1 0 1 1 1)
(0 0 1 1 0 0 1 1)
(1 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  830    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1209    permutation [ 1, 3, 8, 5, 6, 7, 4, 2 ]
vertex  4 -> Algebra 1254    permutation [ 7, 2, 1, 3, 8, 6, 5, 4 ]
vertex  5 -> Algebra 1032    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 1032

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 0 1 1)
(1 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  838    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1230    permutation [ 1, 3, 8, 5, 6, 7, 4, 2 ]
vertex  4 -> Algebra  760    permutation [ 7, 2, 1, 3, 8, 5, 6, 4 ]
vertex  5 -> Algebra 1035    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra 1025    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 1034

Quiver

[ 2, 1 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 5, 7 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 2 ] 
[ 2, 8, 3, 4 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 3, 4, 2, 8 ] 
[ 4, 2, 8, 3 ] - [ 4, 5, 3 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 0 1)
(1 1 1 1 0 0 0 0)
(1 1 1 1 1 0 1 1)
(0 0 1 0 1 0 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  840    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  632    permutation [ 2, 1, 8, 3, 5, 7, 6, 4 ]
vertex  7 -> Algebra  753    permutation [ 5, 2, 1, 8, 3, 7, 6, 4 ]
vertex  8 -> Algebra 1143    permutation [ 2, 1, 3, 8, 5, 7, 6, 4 ]

Algebra 1035

Quiver

[ 2, 1 ], [ 2, 4 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 4, 3, 8, 2 ] 
[ 8, 2, 4, 3 ] 
[ 3, 8, 2, 4 ] 
[ 2, 4, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 0 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  841    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1181    permutation [ 4, 1, 2, 8, 5, 7, 6, 3 ]
vertex  4 -> Algebra 1143    permutation [ 2, 1, 3, 8, 5, 7, 6, 4 ]
vertex  5 -> Algebra  517    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  602    permutation [ 2, 1, 4, 8, 5, 7, 6, 3 ]
vertex  7 -> Algebra 1032    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]

Algebra 1036

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 2, 8, 1 ] 
[ 8, 4, 3 ] 
[ 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1340    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  517    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1119    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1172    permutation [ 1, 3, 4, 8, 6, 7, 5, 2 ]
vertex  5 -> Algebra 1181    permutation [ 4, 1, 2, 8, 5, 7, 6, 3 ]
vertex  6 -> Algebra 1038    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1038

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ]

Relations

[ 2, 8, 1 ] 
[ 8, 4, 3 ] 
[ 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 4, 2 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1345    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  520    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  673    permutation [ 4, 1, 2, 8, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1176    permutation [ 1, 3, 4, 8, 6, 7, 5, 2 ]
vertex  5 -> Algebra  676    permutation [ 4, 1, 2, 8, 5, 6, 7, 3 ]
vertex  6 -> Algebra  521    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1036    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1039

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 5 ] 
[ 1, 2, 4, 8 ] 
[ 5, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 5, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 0 0 1 0 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1347    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  893    permutation [ 3, 4, 8, 7, 6, 1, 2, 5 ]
vertex  3 -> Algebra 1268    permutation [ 1, 4, 3, 8, 5, 7, 6, 2 ]
vertex  4 -> Algebra  521    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1176    permutation [ 1, 3, 4, 8, 6, 7, 5, 2 ]
vertex  7 -> Algebra  522    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1040

Quiver

[ 1, 2 ], [ 2, 4 ], [ 4, 3 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 5 ] 
[ 1, 2, 4, 8 ] 
[ 5, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 5, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1350    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1011    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  522    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  592    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  7 -> Algebra 1268    permutation [ 1, 4, 3, 8, 5, 7, 6, 2 ]

Algebra 1041

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 0 0)
(1 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 1 1 1 1 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  532    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  990    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1043    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1327    permutation [ 1, 3, 8, 2, 6, 7, 5, 4 ]

Algebra 1043

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 0 0)
(1 1 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  534    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  992    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra  525    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1041    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1337    permutation [ 1, 3, 8, 2, 6, 7, 5, 4 ]

Algebra 1044

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 2, 3, 1 ] 
[ 8, 4, 2 ] 
[ 1, 2, 3 ] 
[ 4, 2, 3 ] 
[ 4, 2, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 1 1 0 0 0 1)
(1 1 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1359    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1061    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  841    permutation [ 1, 3, 8, 2, 5, 7, 6, 4 ]
vertex  4 -> Algebra 1269    permutation [ 1, 4, 8, 2, 5, 7, 6, 3 ]
vertex  5 -> Algebra  842    permutation [ 1, 3, 8, 2, 5, 7, 6, 4 ]
vertex  6 -> Algebra 1337    permutation [ 1, 3, 8, 2, 6, 7, 5, 4 ]
vertex  7 -> Algebra  526    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  525    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1045

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 4, 8 ], [ 5, 1 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 5, 1 ] 
[ 4, 8, 3 ] 
[ 5, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 5 ] 
[ 2, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 0)
(1 1 1 1 1 0 0 1)
(0 1 0 1 0 0 0 1)
(1 1 0 0 1 0 0 1)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra  529    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1063    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  941    permutation [ 1, 3, 4, 5, 2, 7, 6, 8 ]
vertex  7 -> Algebra  527    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1469    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1046

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 5, 1 ] 
[ 2, 8, 4 ] 
[ 1, 2, 8, 5 ] 
[ 4, 2, 8 ] 
[ 5, 1, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 5, 1, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 0 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(1 1 0 0 1 0 0 0)
(0 1 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1382    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1052    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1470    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1346    permutation [ 1, 3, 5, 8, 2, 6, 7, 4 ]
vertex  6 -> Algebra 1348    permutation [ 1, 3, 5, 8, 2, 6, 7, 4 ]
vertex  7 -> Algebra 1469    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  527    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1051

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 3, 8 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 6, 5, 2 ] 
[ 5, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 2, 6 ] 
[ 2, 3, 8 ] 
[ 3, 5, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 1 0 0)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 0 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra  874    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1474    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1475    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1455    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1368    permutation [ 2, 6, 7, 5, 1, 8, 4, 3 ]
vertex  7 -> Algebra  530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  529    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1052

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 5, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 5, 1, 2 ] 
[ 1, 2, 5 ] 
[ 2, 8, 6 ] 
[ 1, 2, 8 ] 
[ 6, 2, 8 ] 
[ 2, 5, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 0 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1397    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1476    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1456    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1062    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1477    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1474    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1046    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1053

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 6, 5, 3, 2 ] 
[ 2, 6, 5, 3 ] 
[ 3, 2, 6, 5 ] 
[ 5, 3, 2, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 0 1 1 1 0)
(1 1 1 0 0 1 1 0)
(0 0 0 1 0 0 0 0)
(1 1 1 0 1 0 0 0)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra  876    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1478    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1131    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1473    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1475    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  540    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1057

Quiver

[ 2, 1 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 0 0)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 1 1 1 0 1 1)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  880    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1481    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1457    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1266    permutation [ 7, 2, 1, 3, 8, 4, 6, 5 ]
vertex  6 -> Algebra 1060    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  532    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1060

Quiver

[ 2, 1 ], [ 2, 5 ], [ 3, 8 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 5, 3, 8, 2 ] 
[ 8, 2, 5, 3 ] 
[ 3, 8, 2, 5 ] 
[ 2, 5, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 0 0)
(1 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  883    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1222    permutation [ 5, 1, 2, 8, 4, 6, 7, 3 ]
vertex  4 -> Algebra 1132    permutation [ 2, 1, 5, 4, 8, 6, 7, 3 ]
vertex  5 -> Algebra 1149    permutation [ 2, 1, 3, 8, 4, 6, 7, 5 ]
vertex  6 -> Algebra  535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1057    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  534    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1061

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 1 ] 
[ 8, 5, 3 ] 
[ 2, 8, 5 ] 
[ 3, 8, 5 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 5, 2 ] 
[ 5, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1405    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1085    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1460    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1483    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1222    permutation [ 5, 1, 2, 8, 4, 6, 7, 3 ]
vertex  7 -> Algebra  536    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1044    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1062

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 5, 8, 6 ] 
[ 1, 2, 5, 8 ] 
[ 6, 5, 8 ] 
[ 8, 1, 2, 5 ] - [ 8, 6, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 1 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 1 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1395    permutation [ 2, 8, 1, 7, 4, 5, 3, 6 ]
vertex  2 -> Algebra 1052    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1398    permutation [ 2, 8, 1, 7, 4, 5, 3, 6 ]
vertex  4 -> Algebra 1461    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  536    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1483    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1346    permutation [ 1, 3, 2, 5, 8, 6, 7, 4 ]

Algebra 1063

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 5, 8, 2, 3 ] 
[ 8, 2, 3, 5 ] 
[ 2, 3, 5, 8 ] 
[ 3, 1, 2 ] - [ 3, 5, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 1 0 0 0)
(1 1 1 0 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(0 1 1 0 1 1 0 0)
(0 1 1 0 1 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  539    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1090    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1045    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  537    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1485    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1064

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 2, 3, 1 ] 
[ 8, 5, 2 ] 
[ 1, 2, 3 ] 
[ 5, 2, 3 ] 
[ 5, 2, 8 ] 
[ 3, 1, 2 ] - [ 3, 5, 2 ] 
[ 2, 3, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 1 0 1 0 0 1)
(1 1 1 0 1 0 0 0)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1412    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1070    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  959    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1091    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1470    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1304    permutation [ 1, 3, 5, 8, 2, 6, 7, 4 ]
vertex  7 -> Algebra 1485    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  537    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1065

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 8 ], [ 6, 1 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 6, 1 ] 
[ 5, 8, 3 ] 
[ 6, 8, 3 ] 
[ 8, 3, 5 ] 
[ 1, 2, 6 ] 
[ 2, 6, 8 ] 
[ 6, 1, 2 ] - [ 6, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 6 ] 
[ 3, 5, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 1 0 0)
(1 1 1 0 1 1 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(1 1 0 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  2 -> Algebra  538    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1071    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra 1092    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  949    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  7 -> Algebra  955    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1486    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1067

Quiver

[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 7, 6, 2 ] 
[ 6, 2, 3 ] 
[ 8, 2, 3 ] 
[ 6, 2, 7 ] 
[ 2, 3, 8 ] 
[ 3, 6, 2 ] - [ 3, 8, 2 ] 
[ 2, 3, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 1 0)
(1 1 1 0 1 1 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 1 0 1 1)

Good mutations

vertex  1 -> Algebra  893    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1460    permutation [ 6, 1, 2, 7, 8, 5, 4, 3 ]
vertex  3 -> Algebra 1269    permutation [ 6, 2, 1, 3, 8, 4, 5, 7 ]
vertex  4 -> Algebra 1011    permutation [ 6, 2, 1, 7, 8, 5, 4, 3 ]
vertex  5 -> Algebra 1473    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra  540    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1268    permutation [ 6, 2, 1, 3, 8, 4, 5, 7 ]
vertex  8 -> Algebra  538    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1069

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 3 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 6, 3, 8, 2 ] 
[ 8, 2, 6, 3 ] 
[ 3, 8, 2, 6 ] 
[ 2, 6, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 0 0)
(1 1 1 0 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 0 1 1 0 1)
(0 0 1 0 1 1 1 1)
(1 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra  895    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1488    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1095    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1475    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1487    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  540    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  539    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1070

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 6, 3 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 2, 8, 1 ] 
[ 8, 6, 3 ] 
[ 2, 8, 6 ] 
[ 3, 8, 6 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 
[ 6, 2, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 1)
(1 0 1 0 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1303    permutation [ 1, 6, 2, 7, 8, 5, 4, 3 ]
vertex  2 -> Algebra  540    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1077    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1096    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1478    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1489    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1488    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1064    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1071

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 6, 8, 2, 3 ] 
[ 8, 2, 3, 6 ] 
[ 2, 3, 6, 8 ] 
[ 3, 1, 2 ] - [ 3, 6, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 0 0)
(1 1 1 0 0 1 0 1)
(0 1 0 1 1 1 0 1)
(0 1 0 0 1 1 0 1)
(0 1 0 0 0 1 0 1)
(0 1 1 0 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  541    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1097    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1065    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra  956    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1341    permutation [ 3, 7, 1, 2, 6, 4, 5, 8 ]

Algebra 1077

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 6, 2, 3 ] 
[ 2, 3, 8, 6 ] 
[ 6, 2, 3, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 1 0 0 1)
(1 1 1 0 1 1 1 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra  964    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1103    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1088    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra 1378    permutation [ 1, 8, 7, 6, 3, 5, 4, 2 ]
vertex  7 -> Algebra 1232    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1070    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1085

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 5, 2, 3 ] 
[ 2, 3, 8, 5 ] 
[ 5, 2, 3, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 5, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 0 1)

Good mutations

vertex  3 -> Algebra  970    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1125    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1223    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  706    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  556    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1061    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1087

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 2, 3, 1 ] 
[ 5, 8, 2 ] 
[ 1, 2, 3 ] 
[ 8, 2, 3 ] 
[ 5, 8, 6 ] 
[ 6, 5, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 6, 5 ] 
[ 2, 3, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 1 1 1 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1088    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  971    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1128    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  556    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1223    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1398    permutation [ 2, 3, 1, 7, 4, 8, 5, 6 ]

Algebra 1088

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 3, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 2, 5, 1 ] 
[ 1, 2, 5 ] 
[ 8, 6, 2, 5 ] 
[ 2, 5, 8, 6 ] 
[ 6, 2, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 1 1 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra 1077    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra 1129    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1087    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1492    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1228    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1478    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1090

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 6, 2 ], [ 7, 6 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 1 0 0 0)
(1 1 1 1 1 0 0 1)
(0 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 0 0)
(0 1 1 1 1 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  560    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1063    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  558    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1402    permutation [ 1, 3, 8, 5, 2, 7, 6, 4 ]

Algebra 1091

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 6, 2 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 3, 1 ] 
[ 8, 4, 2 ] 
[ 1, 2, 3 ] 
[ 4, 2, 3 ] 
[ 4, 2, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 1 1 1 0 0 1)
(1 1 1 1 1 0 0 0)
(0 1 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1428    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1096    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra  883    permutation [ 1, 3, 8, 5, 2, 6, 7, 4 ]
vertex  5 -> Algebra 1064    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  884    permutation [ 1, 3, 8, 5, 2, 6, 7, 4 ]
vertex  7 -> Algebra 1402    permutation [ 1, 3, 8, 5, 2, 7, 6, 4 ]
vertex  8 -> Algebra  558    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1092

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ], [ 8, 3 ]

Relations

[ 2, 6, 1 ] 
[ 4, 8, 3 ] 
[ 6, 8, 3 ] 
[ 8, 3, 4 ] 
[ 1, 2, 6 ] 
[ 2, 6, 8 ] 
[ 6, 1, 2 ] - [ 6, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 3, 6 ] 
[ 3, 4, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 1 0 0)
(1 1 1 1 1 1 0 1)
(0 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 1 0 0 0 1 0 1)
(0 1 0 0 0 1 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  2 -> Algebra  559    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1097    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  5 -> Algebra 1065    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  909    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  7 -> Algebra  912    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1461    permutation [ 6, 1, 8, 7, 2, 4, 5, 3 ]

Algebra 1095

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 3 ], [ 7, 6 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 6, 3, 8, 2 ] 
[ 8, 2, 6, 3 ] 
[ 3, 8, 2, 6 ] 
[ 2, 6, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 1 0 0)
(1 1 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 1 1 1 1 1)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  849    permutation [ 2, 7, 1, 6, 8, 4, 5, 3 ]
vertex  2 -> Algebra 1351    permutation [ 1, 7, 2, 6, 8, 4, 5, 3 ]
vertex  5 -> Algebra 1069    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1350    permutation [ 6, 7, 1, 2, 8, 4, 5, 3 ]
vertex  7 -> Algebra  561    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  560    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1096

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 6, 3 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 2, 8, 1 ] 
[ 8, 6, 3 ] 
[ 2, 8, 6 ] 
[ 3, 8, 6 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 
[ 6, 2, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra  813    permutation [ 1, 6, 2, 7, 8, 4, 5, 3 ]
vertex  2 -> Algebra  561    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1103    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  5 -> Algebra 1070    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1307    permutation [ 1, 2, 6, 7, 8, 4, 5, 3 ]
vertex  7 -> Algebra 1351    permutation [ 1, 7, 2, 6, 8, 4, 5, 3 ]
vertex  8 -> Algebra 1091    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1097

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 6, 8 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 6, 8, 2, 3 ] 
[ 8, 2, 3, 6 ] 
[ 2, 3, 6, 8 ] 
[ 3, 1, 2 ] - [ 3, 6, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 0 0)
(1 1 1 0 0 1 0 1)
(0 1 0 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 1 0 0 0 1 0 1)
(0 1 1 0 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  562    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1105    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1071    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1092    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra  913    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1346    permutation [ 3, 7, 1, 2, 6, 4, 5, 8 ]

Algebra 1103

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 6, 2, 3 ] 
[ 2, 3, 8, 6 ] 
[ 6, 2, 3, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra  976    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1077    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra  865    permutation [ 1, 8, 7, 6, 3, 4, 5, 2 ]
vertex  7 -> Algebra 1240    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1096    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1105

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 4, 8, 2, 3 ] 
[ 8, 2, 3, 4 ] 
[ 2, 3, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 4, 8, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 1 0 1 0 0)
(1 1 1 1 0 1 0 1)
(0 1 0 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 1 1 1 0 1 1 0)
(0 1 1 0 0 0 0 1)

Good mutations

vertex  2 -> Algebra  568    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  759    permutation [ 3, 2, 1, 8, 4, 6, 5, 7 ]
vertex  6 -> Algebra 1097    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  790    permutation [ 3, 8, 1, 7, 4, 6, 5, 2 ]
vertex  8 -> Algebra  847    permutation [ 3, 7, 1, 2, 4, 6, 5, 8 ]

Algebra 1119

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 8 ], [ 4, 2 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 4 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 8, 4, 2, 3 ] 
[ 2, 3, 8, 4 ] 
[ 4, 2, 3, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 4, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 0 1)
(1 1 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  4 -> Algebra 1182    permutation [ 5, 1, 2, 3, 4, 7, 6, 8 ]
vertex  5 -> Algebra  675    permutation [ 4, 1, 2, 3, 5, 7, 6, 8 ]
vertex  6 -> Algebra  673    permutation [ 4, 1, 2, 3, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1036    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1124

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 3, 8 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 2, 3, 1 ] 
[ 4, 8, 2 ] 
[ 1, 2, 3 ] 
[ 8, 2, 3 ] 
[ 4, 8, 5 ] 
[ 5, 4, 8 ] 
[ 3, 1, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 4 ] - [ 8, 5, 4 ] 
[ 2, 3, 8 ] - [ 2, 4, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1125    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  840    permutation [ 1, 3, 4, 8, 5, 7, 6, 2 ]
vertex  4 -> Algebra  590    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  677    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  592    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1268    permutation [ 1, 8, 4, 3, 5, 7, 6, 2 ]

Algebra 1125

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 2, 4, 1 ] 
[ 1, 2, 4 ] 
[ 8, 5, 2, 4 ] 
[ 2, 4, 8, 5 ] 
[ 5, 2, 4, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 5, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 1 1 1 1 1 0 1)
(1 1 0 1 1 1 0 1)
(0 1 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 0 1)

Good mutations

vertex  3 -> Algebra 1085    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1124    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1200    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  687    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  593    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1460    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1128

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 5 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ], [ 8, 6 ]

Relations

[ 2, 4, 1 ] 
[ 5, 8, 2 ] 
[ 1, 2, 4 ] 
[ 8, 2, 4 ] 
[ 5, 8, 6 ] 
[ 6, 5, 8 ] 
[ 4, 1, 2 ] - [ 4, 8, 2 ] 
[ 8, 2, 5 ] - [ 8, 6, 5 ] 
[ 2, 4, 8 ] - [ 2, 5, 8 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 1 1 0 0 1)
(1 1 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(0 0 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1129    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1087    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  593    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1200    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1408    permutation [ 2, 3, 1, 7, 4, 8, 5, 6 ]

Algebra 1129

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 2, 5, 1 ] 
[ 1, 2, 5 ] 
[ 8, 6, 2, 5 ] 
[ 2, 5, 8, 6 ] 
[ 6, 2, 5, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 1)
(1 1 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(1 1 0 0 1 1 1 1)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  3 -> Algebra 1088    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1128    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1497    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1206    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1498    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1131

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 7 ], [ 6, 8 ], [ 8, 5 ]

Relations

[ 6, 8, 5, 2 ] 
[ 2, 6, 8, 5 ] 
[ 8, 5, 2, 6 ] 
[ 5, 2, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 0 0 1 1 1)
(1 1 1 1 1 1 1 0)
(1 1 0 1 1 1 1 0)
(1 1 0 0 1 1 1 0)
(0 0 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  958    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1498    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1053    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  5 -> Algebra 1001    permutation [ 1, 2, 4, 5, 8, 6, 7, 3 ]
vertex  6 -> Algebra 1500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1495    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1132

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 1 ], [ 6, 3 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 8, 5, 1 ] 
[ 8, 5, 1, 3 ] 
[ 1, 3, 8, 5 ] 
[ 5, 1, 3, 8 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 0 0 0 0 0 0)
(0 0 1 0 1 0 0 1)
(1 1 1 1 1 0 0 0)
(1 1 1 0 1 0 0 0)
(0 0 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1199    permutation [ 3, 2, 1, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  959    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1137    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex  4 -> Algebra 1060    permutation [ 2, 1, 8, 4, 3, 6, 7, 5 ]
vertex  5 -> Algebra 1009    permutation [ 2, 1, 5, 8, 3, 6, 7, 4 ]
vertex  6 -> Algebra 1010    permutation [ 2, 1, 5, 8, 3, 6, 7, 4 ]
vertex  7 -> Algebra 1457    permutation [ 2, 1, 5, 8, 3, 7, 6, 4 ]

Algebra 1137

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 5 ], [ 5, 1 ], [ 6, 3 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 5, 1, 3 ] 
[ 1, 3, 5 ] 
[ 3, 8, 6 ] 
[ 1, 3, 8 ] 
[ 6, 3, 8 ] 
[ 3, 5, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 6, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 0 1 0 0 1)
(1 1 0 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra  964    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1149    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1144    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  6 -> Algebra 1502    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1259    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1132    permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]

Algebra 1143

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 1 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 4, 1, 3 ] 
[ 1, 3, 4 ] 
[ 3, 8, 5 ] 
[ 1, 3, 8 ] 
[ 5, 3, 8 ] 
[ 3, 4, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 5, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 1 0 0 0 1)
(1 1 0 1 0 0 0 0)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  2 -> Algebra  970    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1034    permutation [ 2, 1, 3, 8, 5, 7, 6, 4 ]
vertex  5 -> Algebra 1255    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  6 -> Algebra  760    permutation [ 5, 1, 2, 3, 4, 6, 7, 8 ]
vertex  7 -> Algebra  612    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1035    permutation [ 2, 1, 3, 8, 5, 7, 6, 4 ]

Algebra 1144

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 4, 1, 3 ] 
[ 5, 8, 1, 3 ] 
[ 1, 3, 4 ] 
[ 5, 8, 6 ] 
[ 1, 3, 5, 8 ] 
[ 6, 5, 8 ] 
[ 3, 4, 1 ] - [ 3, 5, 8, 1 ] 
[ 8, 1, 3, 5 ] - [ 8, 6, 5 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(1 1 0 1 0 0 0 0)
(1 1 0 0 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra  971    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1137    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  5 -> Algebra  612    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1255    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1009    permutation [ 2, 1, 3, 5, 8, 6, 7, 4 ]

Algebra 1149

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 6, 3 ], [ 6, 7 ], [ 8, 1 ], [ 8, 6 ]

Relations

[ 4, 1, 3 ] 
[ 1, 3, 4 ] 
[ 3, 8, 6 ] 
[ 1, 3, 8 ] 
[ 6, 3, 8 ] 
[ 3, 4, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 6, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(1 1 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra  976    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1137    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1368    permutation [ 1, 8, 7, 6, 2, 4, 5, 3 ]
vertex  7 -> Algebra 1266    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1060    permutation [ 2, 1, 3, 5, 8, 6, 7, 4 ]

Algebra 1164

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 4, 8, 1 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 0 0 0)
(1 0 0 1 1 1 0 0)
(1 0 0 1 1 1 1 0)
(1 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1254    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1221    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra  829    permutation [ 2, 3, 4, 8, 7, 6, 1, 5 ]
vertex  7 -> Algebra  654    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  830    permutation [ 2, 3, 4, 8, 7, 6, 1, 5 ]

Algebra 1165

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 6, 8, 1 ] 
[ 5, 3, 4 ] 
[ 6, 8, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 6, 8 ] 
[ 3, 4, 6, 8 ] 
[ 4, 5, 3 ] - [ 4, 6, 8, 3 ] 
[ 8, 1, 6 ] - [ 8, 3, 4, 6 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 1 0 1 0 0)
(0 0 1 1 0 1 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 0 1 0 0 0)
(0 0 1 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 0 1 1 0 1 0 1)

Good mutations

vertex  2 -> Algebra 1255    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1223    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1169    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra  970    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  7 -> Algebra  971    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra  806    permutation [ 2, 3, 4, 6, 8, 7, 1, 5 ]

Algebra 1169

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 4, 8, 1 ] 
[ 6, 3, 4 ] 
[ 3, 4, 6 ] 
[ 1, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 6, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 0 0 1 0 1 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 0 0 0 0)
(0 0 1 1 0 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(1 0 0 1 0 1 1 0)
(1 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1259    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1232    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1174    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1165    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra  964    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1298    permutation [ 2, 3, 6, 4, 8, 7, 1, 5 ]

Algebra 1172

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 7 ], [ 5, 6 ], [ 6, 7 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 1 ] 
[ 1, 8, 3, 4 ] 
[ 7, 3, 4 ] 
[ 3, 4, 7 ] 
[ 3, 4, 1, 8 ] 
[ 4, 1, 8, 3 ] - [ 4, 7, 3 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 1 1 0 0 1 1)
(0 0 1 0 1 1 1 0)
(0 0 1 0 0 1 1 0)
(0 0 1 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1450    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1262    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1036    permutation [ 1, 8, 2, 3, 7, 5, 6, 4 ]
vertex  5 -> Algebra 1176    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1449    permutation [ 2, 3, 5, 6, 7, 1, 8, 4 ]

Algebra 1173

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 1 ]

Relations

[ 4, 3, 8, 1 ] 
[ 8, 1, 4, 3 ] 
[ 3, 8, 1, 4 ] 
[ 1, 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 1 1 0 1 1 1)
(0 0 1 1 0 0 1 1)
(1 0 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1263    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  990    permutation [ 1, 4, 2, 8, 7, 5, 6, 3 ]
vertex  4 -> Algebra 1449    permutation [ 2, 3, 5, 6, 7, 1, 8, 4 ]
vertex  5 -> Algebra 1177    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 1174

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 5, 6 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 4, 8, 1 ] 
[ 5, 3, 4 ] 
[ 3, 4, 5 ] 
[ 1, 4, 8 ] 
[ 3, 4, 8 ] 
[ 4, 5, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 1 0 1)
(0 0 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 0 0 1 1 1 1 0)
(1 0 1 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1266    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1240    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1169    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  976    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra  880    permutation [ 2, 3, 4, 6, 8, 7, 1, 5 ]

Algebra 1176

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 7 ], [ 5, 6 ], [ 5, 7 ], [ 7, 3 ], [ 8, 3 ]

Relations

[ 8, 3, 4, 1 ] 
[ 1, 8, 3, 4 ] 
[ 7, 3, 4 ] 
[ 3, 4, 7 ] 
[ 3, 4, 1, 8 ] 
[ 4, 1, 8, 3 ] - [ 4, 7, 3 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(1 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 0 1 1 0 0 1 1)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 1 0 0)
(0 0 1 0 0 0 1 0)
(0 0 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1452    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1183    permutation [ 7, 1, 8, 4, 2, 5, 6, 3 ]
vertex  3 -> Algebra 1038    permutation [ 1, 8, 2, 3, 7, 5, 6, 4 ]
vertex  5 -> Algebra 1039    permutation [ 1, 8, 2, 3, 7, 5, 6, 4 ]
vertex  6 -> Algebra 1172    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1393    permutation [ 2, 3, 7, 6, 4, 1, 8, 5 ]

Algebra 1177

Quiver

[ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 1 ]

Relations

[ 4, 3, 8, 1 ] 
[ 8, 1, 4, 3 ] 
[ 3, 8, 1, 4 ] 
[ 1, 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 1)
(0 0 0 0 0 1 0 0)
(0 0 1 1 0 0 1 1)
(1 0 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1267    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  992    permutation [ 1, 4, 2, 8, 7, 5, 6, 3 ]
vertex  4 -> Algebra 1393    permutation [ 2, 3, 7, 6, 4, 1, 8, 5 ]
vertex  5 -> Algebra  993    permutation [ 1, 4, 2, 8, 7, 5, 6, 3 ]
vertex  6 -> Algebra 1173    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 1178

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 1 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(1 1 1 1 0 0 0 1)
(1 0 1 1 1 0 0 0)
(1 0 1 1 1 1 1 0)
(1 0 1 1 1 0 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  6 -> Algebra 1180    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1209    permutation [ 2, 8, 4, 6, 7, 5, 1, 3 ]

Algebra 1180

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(1 1 1 1 0 0 0 1)
(1 0 1 1 1 0 0 0)
(1 0 1 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  6 -> Algebra  675    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1178    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1230    permutation [ 2, 8, 4, 6, 7, 5, 1, 3 ]

Algebra 1181

Quiver

[ 1, 3 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 2 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 3, 4, 1 ] 
[ 8, 4, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 4, 1, 8 ] 
[ 4, 1, 3 ] - [ 4, 2, 3 ] 
[ 1, 3, 4 ] - [ 1, 8, 4 ] 

Cartan matrix

(1 0 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1359    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1035    permutation [ 2, 3, 8, 1, 5, 7, 6, 4 ]
vertex  5 -> Algebra 1036    permutation [ 2, 3, 8, 1, 5, 7, 6, 4 ]
vertex  6 -> Algebra 1230    permutation [ 2, 8, 4, 6, 7, 5, 1, 3 ]
vertex  7 -> Algebra  676    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  675    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1182

Quiver

[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 4, 8 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 5, 8, 1 ] 
[ 3, 4, 2 ] 
[ 5, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 1, 5, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 5 ] - [ 8, 3, 5 ] 
[ 3, 4, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 1)
(1 0 0 0 1 1 0 0)
(1 0 0 0 1 1 1 0)
(1 0 1 0 1 0 0 1)

Good mutations

vertex  3 -> Algebra 1198    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  4 -> Algebra  829    permutation [ 2, 4, 5, 8, 7, 6, 1, 3 ]
vertex  5 -> Algebra 1119    permutation [ 2, 3, 4, 5, 1, 7, 6, 8 ]
vertex  7 -> Algebra  677    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1262    permutation [ 2, 8, 5, 4, 7, 6, 1, 3 ]

Algebra 1183

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 2 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 8, 4, 1 ] 
[ 3, 8, 4, 2 ] 
[ 8, 4, 2, 3 ] 
[ 1, 8, 4 ] 
[ 2, 3, 8, 4 ] 
[ 4, 1, 8 ] - [ 4, 2, 3, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 1 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 0 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra 1362    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1473    permutation [ 5, 8, 1, 7, 4, 2, 3, 6 ]
vertex  5 -> Algebra 1176    permutation [ 2, 5, 8, 4, 6, 7, 1, 3 ]
vertex  6 -> Algebra 1268    permutation [ 2, 8, 5, 4, 1, 7, 6, 3 ]
vertex  7 -> Algebra 1262    permutation [ 2, 8, 5, 4, 7, 6, 1, 3 ]
vertex  8 -> Algebra  677    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1198

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 3, 5, 8, 1 ] 
[ 3, 5, 2 ] 
[ 2, 3, 5 ] 
[ 8, 1, 3, 5 ] 
[ 1, 3, 5, 8 ] 
[ 5, 2, 3 ] - [ 5, 8, 1, 3 ] 

Cartan matrix

(1 0 1 0 1 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 0 1 0 0 1)
(1 1 1 1 1 0 0 1)
(1 1 1 0 1 0 0 1)
(1 0 1 0 1 1 0 0)
(1 0 1 0 1 1 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra 1221    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1182    permutation [ 1, 2, 5, 4, 3, 6, 7, 8 ]
vertex  7 -> Algebra  687    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1508    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1199

Quiver

[ 1, 3 ], [ 1, 8 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ], [ 6, 1 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 5, 1 ] 
[ 8, 5, 1 ] 
[ 3, 5, 2 ] 
[ 2, 3, 5 ] 
[ 5, 1, 8 ] 
[ 5, 1, 3 ] - [ 5, 2, 3 ] 
[ 1, 3, 5 ] - [ 1, 8, 5 ] 

Cartan matrix

(1 0 1 0 1 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 0 1 0 0 0)
(1 1 1 1 1 0 0 0)
(1 1 1 0 1 0 0 0)
(1 0 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra 1412    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1132    permutation [ 3, 2, 1, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1222    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1473    permutation [ 3, 5, 1, 7, 4, 2, 8, 6 ]
vertex  6 -> Algebra 1460    permutation [ 2, 3, 5, 8, 1, 6, 7, 4 ]
vertex  7 -> Algebra 1508    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  687    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1200

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 2 ], [ 5, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 6, 8, 1 ] 
[ 3, 5, 2 ] 
[ 6, 8, 3 ] 
[ 2, 3, 5 ] 
[ 8, 3, 5 ] 
[ 1, 6, 8 ] 
[ 5, 2, 3 ] - [ 5, 8, 3 ] 
[ 8, 1, 6 ] - [ 8, 3, 6 ] 
[ 3, 5, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 0 0 1 0 0)
(0 0 1 0 1 1 0 1)
(1 1 1 1 1 1 0 1)
(1 1 1 0 1 1 0 1)
(0 0 0 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 0 1 0 0 1 0 1)

Good mutations

vertex  3 -> Algebra 1206    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra 1223    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1125    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  7 -> Algebra 1128    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1447    permutation [ 3, 4, 7, 1, 2, 8, 6, 5 ]

Algebra 1206

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ]

Relations

[ 3, 6, 8, 1 ] 
[ 3, 6, 2 ] 
[ 2, 3, 6 ] 
[ 8, 1, 3, 6 ] 
[ 1, 3, 6, 8 ] 
[ 6, 2, 3 ] - [ 6, 8, 1, 3 ] 

Cartan matrix

(1 0 1 0 0 1 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 0 0 1 0 1)
(1 1 1 1 1 1 0 1)
(1 1 1 0 1 1 0 1)
(1 1 1 0 0 1 0 1)
(1 0 1 0 0 1 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra 1228    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1200    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1129    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1512    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1209

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 7 ], [ 4, 5 ], [ 5, 6 ], [ 6, 7 ], [ 7, 2 ], [ 7, 8 ], [ 8, 3 ]

Relations

[ 8, 3, 1 ] 
[ 3, 7, 2 ] 
[ 1, 8, 3 ] 
[ 2, 3, 7 ] 
[ 8, 3, 7 ] 
[ 7, 2, 3 ] - [ 7, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 7, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 1 1)
(0 1 1 1 1 1 1 1)
(0 1 1 0 1 1 1 1)
(0 1 1 0 0 1 1 1)
(0 1 1 0 0 0 1 1)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1499    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1178    permutation [ 7, 1, 8, 3, 6, 4, 5, 2 ]
vertex  4 -> Algebra 1230    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  8 -> Algebra 1025    permutation [ 1, 8, 2, 7, 4, 5, 6, 3 ]

Algebra 1221

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 0 1 1 1 1 0 0)
(1 0 1 1 1 1 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra 1164    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1198    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  7 -> Algebra  706    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1481    permutation [ 2, 3, 8, 5, 1, 7, 6, 4 ]

Algebra 1222

Quiver

[ 1, 3 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 2 ], [ 4, 5 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 3, 4, 1 ] 
[ 8, 4, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 4, 1, 8 ] 
[ 4, 1, 3 ] - [ 4, 2, 3 ] 
[ 1, 3, 4 ] - [ 1, 8, 4 ] 

Cartan matrix

(1 0 1 1 1 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 1 0 0 0)
(1 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 0 0 1)

Good mutations

vertex  2 -> Algebra 1428    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1060    permutation [ 2, 3, 8, 5, 1, 6, 7, 4 ]
vertex  4 -> Algebra 1337    permutation [ 2, 8, 3, 4, 6, 7, 1, 5 ]
vertex  5 -> Algebra 1199    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1061    permutation [ 2, 3, 8, 5, 1, 6, 7, 4 ]
vertex  7 -> Algebra 1481    permutation [ 2, 3, 8, 5, 1, 7, 6, 4 ]
vertex  8 -> Algebra  706    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1223

Quiver

[ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 6, 8, 1 ] 
[ 3, 4, 2 ] 
[ 6, 8, 3 ] 
[ 2, 3, 4 ] 
[ 8, 3, 4 ] 
[ 1, 6, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 3 ] 
[ 8, 1, 6 ] - [ 8, 3, 6 ] 
[ 3, 4, 8 ] - [ 3, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 0 0 1 0 0)
(0 0 1 1 1 1 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 0 1 0 0 1 0 1)

Good mutations

vertex  3 -> Algebra 1228    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra 1165    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1200    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1085    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  7 -> Algebra 1087    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1517    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1228

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 4, 6 ], [ 6, 2 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ]

Relations

[ 3, 6, 8, 1 ] 
[ 3, 6, 2 ] 
[ 2, 3, 6 ] 
[ 8, 1, 3, 6 ] 
[ 1, 3, 6, 8 ] 
[ 6, 2, 3 ] - [ 6, 8, 1, 3 ] 

Cartan matrix

(1 0 1 0 0 1 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 0 0 1 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(1 1 1 0 0 1 0 1)
(1 0 1 0 0 1 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra 1232    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra 1206    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1223    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1088    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1382    permutation [ 6, 2, 7, 8, 3, 4, 5, 1 ]

Algebra 1230

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 7 ], [ 4, 5 ], [ 4, 6 ], [ 6, 7 ], [ 7, 2 ], [ 7, 8 ], [ 8, 3 ]

Relations

[ 8, 3, 1 ] 
[ 3, 7, 2 ] 
[ 1, 8, 3 ] 
[ 2, 3, 7 ] 
[ 8, 3, 7 ] 
[ 7, 2, 3 ] - [ 7, 8, 3 ] 
[ 3, 1, 8 ] - [ 3, 7, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 1 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 1 0 0 0)
(0 1 1 0 0 1 1 1)
(0 1 1 0 0 0 1 1)
(0 0 1 0 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1493    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1180    permutation [ 7, 1, 8, 3, 6, 4, 5, 2 ]
vertex  4 -> Algebra 1181    permutation [ 7, 1, 8, 3, 6, 4, 5, 2 ]
vertex  5 -> Algebra 1209    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  8 -> Algebra 1032    permutation [ 1, 8, 2, 7, 4, 5, 6, 3 ]

Algebra 1232

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 7, 1 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 0 1 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 1 0 1)
(1 1 1 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 0 1 1 0 1 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra 1169    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1240    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1228    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1077    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1488    permutation [ 2, 3, 8, 5, 6, 1, 7, 4 ]

Algebra 1240

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 5, 6 ], [ 7, 1 ], [ 8, 1 ]

Relations

[ 3, 4, 8, 1 ] 
[ 3, 4, 2 ] 
[ 2, 3, 4 ] 
[ 8, 1, 3, 4 ] 
[ 1, 3, 4, 8 ] 
[ 4, 2, 3 ] - [ 4, 8, 1, 3 ] 

Cartan matrix

(1 0 1 1 1 1 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 1 1 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 0 1 1 1 1 1 0)
(1 0 1 0 0 0 0 1)

Good mutations

vertex  4 -> Algebra 1174    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1232    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1103    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1351    permutation [ 2, 7, 3, 1, 4, 5, 6, 8 ]

Algebra 1243

Quiver

[ 1, 3 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ], [ 8, 4 ]

Relations

[ 3, 8, 4, 1 ] 
[ 3, 8, 2 ] 
[ 1, 3, 8, 4 ] 
[ 2, 3, 8 ] 
[ 4, 1, 3, 8 ] 
[ 8, 2, 3 ] - [ 8, 4, 1, 3 ] 

Cartan matrix

(1 0 1 0 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 1 0 0 1)
(1 0 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  731    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  781    permutation [ 4, 1, 2, 3, 5, 7, 6, 8 ]
vertex  6 -> Algebra  779    permutation [ 4, 1, 2, 3, 5, 7, 6, 8 ]

Algebra 1254

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 6, 1 ], [ 7, 6 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 4, 8, 1 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 1, 4, 8 ] 
[ 2, 4, 8 ] 
[ 4, 5, 2 ] - [ 4, 8, 2 ] 
[ 8, 1, 4 ] - [ 8, 2, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 0)
(1 0 0 1 1 1 0 0)
(1 0 0 1 1 1 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  3 -> Algebra 1164    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1024    permutation [ 3, 2, 4, 8, 7, 6, 1, 5 ]
vertex  7 -> Algebra  760    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1025    permutation [ 3, 2, 4, 8, 7, 6, 1, 5 ]

Algebra 1255

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 2 ], [ 6, 8 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 6, 8, 1 ] 
[ 5, 2, 4 ] 
[ 6, 8, 2, 4 ] 
[ 2, 4, 5 ] 
[ 1, 6, 8 ] 
[ 2, 4, 6, 8 ] 
[ 4, 5, 2 ] - [ 4, 6, 8, 2 ] 
[ 8, 1, 6 ] - [ 8, 2, 4, 6 ] 

Cartan matrix

(1 0 0 0 0 1 0 0)
(0 1 1 1 0 1 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 1 1 0 1 0 0 0)
(0 1 1 0 0 1 0 1)
(1 0 0 0 0 1 1 0)
(1 1 1 1 0 1 0 1)

Good mutations

vertex  3 -> Algebra 1165    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1259    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  6 -> Algebra 1143    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  7 -> Algebra 1144    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1005    permutation [ 3, 2, 4, 6, 8, 7, 1, 5 ]

Algebra 1259

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 2 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 4, 8, 1 ] 
[ 6, 2, 4 ] 
[ 2, 4, 6 ] 
[ 1, 4, 8 ] 
[ 2, 4, 8 ] 
[ 4, 6, 2 ] - [ 4, 8, 2 ] 
[ 8, 1, 4 ] - [ 8, 2, 4 ] 

Cartan matrix

(1 0 0 1 0 1 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 0 1 0 1)
(0 1 1 0 1 1 0 0)
(0 1 1 0 0 1 0 0)
(1 0 0 1 0 1 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  3 -> Algebra 1169    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1266    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra 1255    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  7 -> Algebra 1137    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1457    permutation [ 3, 2, 6, 4, 8, 7, 1, 5 ]

Algebra 1262

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 4, 7 ], [ 5, 6 ], [ 6, 7 ], [ 7, 2 ], [ 8, 2 ]

Relations

[ 8, 2, 4, 1 ] 
[ 1, 8, 2, 4 ] 
[ 7, 2, 4 ] 
[ 2, 4, 7 ] 
[ 2, 4, 1, 8 ] 
[ 4, 1, 8, 2 ] - [ 4, 7, 2 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 0 0 1 1)
(0 1 1 0 1 1 1 0)
(0 1 1 0 0 1 1 0)
(0 1 1 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1501    permutation [ 2, 3, 4, 5, 6, 7, 1, 8 ]
vertex  2 -> Algebra 1182    permutation [ 7, 1, 8, 4, 3, 6, 5, 2 ]
vertex  3 -> Algebra 1172    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1183    permutation [ 7, 1, 8, 4, 3, 6, 5, 2 ]
vertex  8 -> Algebra 1500    permutation [ 3, 2, 5, 6, 7, 1, 8, 4 ]

Algebra 1263

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 8 ], [ 4, 2 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 1 ]

Relations

[ 4, 2, 8, 1 ] 
[ 8, 1, 4, 2 ] 
[ 2, 8, 1, 4 ] 
[ 1, 4, 2, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 1 1 0 0 0 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 0 1 1 1)
(0 1 1 1 0 0 1 1)
(1 0 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1327    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1173    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1500    permutation [ 3, 2, 5, 6, 7, 1, 8, 4 ]
vertex  5 -> Algebra 1267    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 1266

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 4, 5 ], [ 4, 8 ], [ 5, 2 ], [ 5, 6 ], [ 7, 1 ], [ 8, 1 ], [ 8, 2 ]

Relations

[ 4, 8, 1 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 1, 4, 8 ] 
[ 2, 4, 8 ] 
[ 4, 5, 2 ] - [ 4, 8, 2 ] 
[ 8, 1, 4 ] - [ 8, 2, 4 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 1 1 0 1)
(0 1 1 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(1 0 0 1 1 1 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  3 -> Algebra 1174    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1259    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra 1149    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1057    permutation [ 3, 2, 4, 6, 8, 7, 1, 5 ]

Algebra 1267

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 8 ], [ 4, 2 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 1 ]

Relations

[ 4, 2, 8, 1 ] 
[ 8, 1, 4, 2 ] 
[ 2, 8, 1, 4 ] 
[ 1, 4, 2, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 1 1 0 0 0 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 0 0)
(0 1 1 1 0 0 1 1)
(1 0 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1337    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1177    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1473    permutation [ 3, 2, 7, 6, 4, 1, 8, 5 ]
vertex  5 -> Algebra 1269    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra 1263    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 1268

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 4, 5 ], [ 5, 2 ], [ 5, 7 ], [ 6, 7 ], [ 8, 2 ]

Relations

[ 8, 2, 4, 1 ] 
[ 1, 8, 2, 4 ] 
[ 5, 2, 4 ] 
[ 2, 4, 5 ] 
[ 2, 4, 1, 8 ] 
[ 4, 1, 8, 2 ] - [ 4, 5, 2 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(1 1 1 1 0 0 0 0)
(0 0 1 0 0 0 0 0)
(1 1 1 1 1 0 1 1)
(0 1 1 0 1 0 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1487    permutation [ 3, 2, 4, 6, 7, 8, 1, 5 ]
vertex  2 -> Algebra 1124    permutation [ 1, 8, 4, 3, 5, 7, 6, 2 ]
vertex  3 -> Algebra 1039    permutation [ 1, 8, 3, 2, 5, 7, 6, 4 ]
vertex  6 -> Algebra 1040    permutation [ 1, 8, 3, 2, 5, 7, 6, 4 ]
vertex  7 -> Algebra 1183    permutation [ 5, 1, 8, 4, 3, 7, 6, 2 ]
vertex  8 -> Algebra 1067    permutation [ 3, 2, 4, 6, 7, 1, 8, 5 ]

Algebra 1269

Quiver

[ 1, 4 ], [ 2, 3 ], [ 2, 8 ], [ 4, 2 ], [ 5, 4 ], [ 5, 7 ], [ 6, 7 ], [ 8, 1 ]

Relations

[ 4, 2, 8, 1 ] 
[ 8, 1, 4, 2 ] 
[ 2, 8, 1, 4 ] 
[ 1, 4, 2, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 0)
(1 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 1 1 0 0 0 1)
(0 1 1 1 1 0 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 0 0 0 1)

Good mutations

vertex  2 -> Algebra 1044    permutation [ 1, 4, 8, 2, 5, 7, 6, 3 ]
vertex  3 -> Algebra  993    permutation [ 1, 4, 3, 8, 5, 7, 6, 2 ]
vertex  4 -> Algebra 1067    permutation [ 3, 2, 4, 6, 7, 1, 8, 5 ]
vertex  5 -> Algebra  774    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  994    permutation [ 1, 4, 3, 8, 5, 7, 6, 2 ]
vertex  7 -> Algebra 1267    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]

Algebra 1270

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(1 1 0 1 1 0 0 0)
(1 1 0 1 1 1 1 0)
(1 1 0 1 1 0 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  787    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  990    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1271    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1271

Quiver

[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 6, 5 ], [ 6, 7 ], [ 8, 1 ], [ 8, 3 ]

Relations

[ 2, 4, 8, 1 ] 
[ 4, 8, 1, 2 ] 
[ 4, 8, 3 ] 
[ 1, 2, 4, 8 ] 
[ 3, 4, 8 ] 
[ 8, 1, 2, 4 ] - [ 8, 3, 4 ] 

Cartan matrix

(1 1 0 1 0 0 0 0)
(0 1 0 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(1 0 0 1 0 0 0 1)
(1 1 0 1 1 0 0 0)
(1 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra  789    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  992    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  781    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1270    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1291

Quiver

[ 1, 2 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 2, 4, 3 ] 
[ 3, 2, 4 ] 
[ 5, 2, 4 ] 
[ 5, 2, 6 ] 
[ 4, 3, 2 ] - [ 4, 5, 2 ] 
[ 2, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 1 0 1 1 1 0 0)
(0 1 0 1 1 1 0 0)
(0 1 1 0 0 1 0 0)
(0 1 1 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1455    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1442    permutation [ 1, 2, 8, 3, 4, 6, 7, 5 ]
vertex  5 -> Algebra  812    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1451    permutation [ 1, 2, 4, 8, 3, 5, 7, 6 ]
vertex  7 -> Algebra  802    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  874    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1292

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 6, 2 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 4, 3, 1 ] 
[ 6, 2, 3, 1 ] 
[ 3, 1, 6, 2 ] 
[ 8, 6, 2 ] 
[ 3, 1, 4 ] 
[ 6, 2, 8 ] 
[ 1, 4, 3 ] - [ 1, 6, 2, 3 ] 
[ 2, 3, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 1 1 1 1 0)
(1 1 1 0 1 1 1 1)
(1 0 1 0 1 1 1 0)
(0 0 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1294    permutation [ 2, 6, 1, 8, 7, 3, 5, 4 ]
vertex  2 -> Algebra 1294    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1528    permutation [ 2, 1, 6, 8, 7, 3, 5, 4 ]
vertex  7 -> Algebra 1528    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1294

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 1 ], [ 2, 3 ], [ 2, 5 ], [ 3, 6 ], [ 4, 2 ], [ 6, 2 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 4, 2, 1 ] 
[ 6, 2, 1 ] 
[ 3, 6, 2 ] 
[ 6, 2, 3 ] 
[ 2, 1, 4 ] 
[ 1, 4, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 6 ] - [ 2, 3, 6 ] 

Cartan matrix

(1 1 0 1 1 1 1 0)
(1 1 1 0 1 1 1 0)
(0 0 1 0 0 1 1 0)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1531    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  802    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1292    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1517    permutation [ 3, 4, 1, 2, 5, 7, 8, 6 ]
vertex  5 -> Algebra 1308    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1530    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  875    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1297

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 5 ]

Relations

[ 3, 2, 1 ] 
[ 5, 2, 1 ] 
[ 8, 5, 2 ] 
[ 2, 1, 3 ] 
[ 5, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 5, 2 ] 
[ 2, 1, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 1 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 1 0 1 1 0 1 0)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  958    permutation [ 3, 1, 6, 7, 5, 2, 4, 8 ]
vertex  2 -> Algebra  806    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1532    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1341    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1517    permutation [ 7, 1, 3, 5, 8, 4, 6, 2 ]
vertex  6 -> Algebra 1302    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  956    permutation [ 3, 1, 6, 7, 5, 2, 4, 8 ]

Algebra 1298

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 4, 3, 2 ] 
[ 2, 5, 4, 3 ] 
[ 3, 2, 5, 4 ] 
[ 4, 3, 2, 5 ] 

Cartan matrix

(1 1 0 1 1 0 0 0)
(0 1 0 1 1 0 0 0)
(0 1 1 0 1 0 0 0)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 1 1 0 1 0)
(0 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1457    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1485    permutation [ 1, 5, 2, 8, 3, 7, 6, 4 ]
vertex  3 -> Algebra  806    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1169    permutation [ 7, 1, 2, 4, 8, 3, 6, 5 ]
vertex  6 -> Algebra  959    permutation [ 1, 2, 5, 8, 3, 7, 6, 4 ]
vertex  8 -> Algebra  880    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1302

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 5, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 2, 1 ] 
[ 5, 2, 1 ] 
[ 8, 5, 2 ] 
[ 2, 1, 3 ] 
[ 5, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 5, 2 ] 
[ 2, 1, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 0 1 1 0 0 0)
(0 1 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra  876    permutation [ 3, 1, 5, 7, 8, 2, 4, 6 ]
vertex  2 -> Algebra  810    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1470    permutation [ 1, 5, 4, 8, 3, 6, 7, 2 ]
vertex  4 -> Algebra 1346    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1398    permutation [ 3, 5, 1, 7, 8, 2, 4, 6 ]
vertex  6 -> Algebra  811    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1297    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  913    permutation [ 3, 1, 6, 7, 5, 2, 4, 8 ]

Algebra 1303

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 3, 1 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 5, 2, 3, 1 ] 
[ 3, 1, 5, 2 ] 
[ 8, 5, 2 ] 
[ 1, 5, 2, 3 ] 
[ 5, 2, 8 ] 
[ 2, 3, 1, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 0 1 1 1 0 0)
(1 1 1 1 1 1 0 1)
(1 0 1 0 1 1 0 0)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1070    permutation [ 1, 3, 8, 7, 6, 2, 4, 5 ]
vertex  2 -> Algebra 1304    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  811    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1348    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1416    permutation [ 3, 5, 8, 7, 6, 2, 4, 1 ]
vertex  6 -> Algebra 1470    permutation [ 1, 5, 4, 8, 3, 6, 7, 2 ]
vertex  7 -> Algebra  813    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1304

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 3, 5, 2 ] 
[ 3, 5, 4 ] 
[ 4, 3, 5 ] 
[ 5, 2, 3 ] - [ 5, 4, 3 ] 
[ 2, 1, 5 ] - [ 2, 3, 5 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(0 0 1 0 1 1 0 0)
(0 0 1 1 0 0 0 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1489    permutation [ 1, 2, 8, 7, 6, 3, 4, 5 ]
vertex  2 -> Algebra  812    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1303    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  949    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1534    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1064    permutation [ 1, 5, 2, 8, 3, 6, 7, 4 ]
vertex  7 -> Algebra  815    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  884    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1305

Quiver

[ 1, 2 ], [ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 2, 5 ], [ 3, 1 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 3, 1, 2 ] 
[ 5, 1, 2 ] 
[ 1, 2, 3 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 2, 3, 1 ] - [ 2, 5, 1 ] 
[ 1, 2, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 1 0 1 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 0 1 0 0 1 1 0)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1428    permutation [ 1, 5, 8, 6, 7, 2, 4, 3 ]
vertex  2 -> Algebra 1528    permutation [ 5, 1, 6, 8, 7, 2, 3, 4 ]
vertex  4 -> Algebra 1352    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  813    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1416    permutation [ 3, 5, 8, 7, 6, 2, 4, 1 ]

Algebra 1307

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 2, 3, 5, 1 ] 
[ 3, 5, 1, 2 ] 
[ 3, 5, 4 ] 
[ 1, 2, 3, 5 ] 
[ 4, 3, 5 ] 
[ 5, 1, 2, 3 ] - [ 5, 4, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 1 1 1 0)
(1 0 1 0 1 1 1 0)
(0 0 1 1 0 0 0 0)
(1 1 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  815    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1012    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1096    permutation [ 1, 2, 8, 6, 7, 3, 4, 5 ]
vertex  5 -> Algebra 1406    permutation [ 1, 8, 2, 7, 3, 5, 4, 6 ]
vertex  7 -> Algebra 1489    permutation [ 1, 2, 8, 7, 6, 3, 4, 5 ]
vertex  8 -> Algebra  885    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1308

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 1 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 4, 5, 1 ] 
[ 6, 5, 1 ] 
[ 6, 5, 3 ] 
[ 5, 1, 4 ] 
[ 3, 6, 5 ] 
[ 1, 4, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 3, 6 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 0 1 1 1 0)
(0 0 1 0 0 1 1 0)
(0 0 1 1 1 0 0 0)
(1 0 1 0 1 1 1 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1294    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1528    permutation [ 3, 1, 6, 8, 7, 5, 2, 4 ]
vertex  4 -> Algebra 1447    permutation [ 1, 2, 8, 3, 4, 6, 7, 5 ]
vertex  5 -> Algebra  815    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1534    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  886    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1327

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 4 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 8, 4, 2 ] 
[ 8, 4, 3 ] 
[ 3, 8, 4 ] 
[ 2, 1, 4 ] - [ 2, 8, 4 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 0 1 0 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 0 1 1 1)
(0 1 1 1 0 0 1 1)
(0 0 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1499    permutation [ 3, 8, 5, 6, 7, 4, 2, 1 ]
vertex  2 -> Algebra  830    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1041    permutation [ 1, 4, 2, 8, 7, 5, 6, 3 ]
vertex  4 -> Algebra 1481    permutation [ 1, 3, 2, 8, 7, 5, 6, 4 ]
vertex  5 -> Algebra 1337    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1263    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1337

Quiver

[ 1, 4 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 4, 3 ], [ 5, 6 ], [ 5, 7 ], [ 7, 4 ], [ 8, 4 ]

Relations

[ 4, 2, 1 ] 
[ 1, 4, 2 ] 
[ 8, 4, 2 ] 
[ 8, 4, 3 ] 
[ 3, 8, 4 ] 
[ 2, 1, 4 ] - [ 2, 8, 4 ] 
[ 4, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 1)
(0 0 1 0 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 1 1 1 1 1 1 1)
(0 0 0 0 0 1 0 0)
(0 1 1 1 0 0 1 1)
(0 0 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1493    permutation [ 3, 8, 5, 6, 7, 4, 2, 1 ]
vertex  2 -> Algebra  838    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1043    permutation [ 1, 4, 2, 8, 7, 5, 6, 3 ]
vertex  4 -> Algebra 1222    permutation [ 7, 1, 3, 4, 8, 5, 6, 2 ]
vertex  5 -> Algebra 1044    permutation [ 1, 4, 2, 8, 7, 5, 6, 3 ]
vertex  6 -> Algebra 1327    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra 1267    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1340

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 1 ], [ 4, 3 ], [ 4, 5 ], [ 6, 7 ], [ 7, 5 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 8, 4, 3 ] 
[ 1, 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 4, 1, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 1 1 0 0 1)
(0 0 1 0 0 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 1 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  842    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1036    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1450    permutation [ 3, 4, 8, 6, 7, 5, 2, 1 ]
vertex  5 -> Algebra 1359    permutation [ 4, 1, 2, 8, 5, 7, 6, 3 ]
vertex  6 -> Algebra 1345    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1341

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 5 ]

Relations

[ 3, 4, 1 ] 
[ 5, 4, 1 ] 
[ 4, 1, 3 ] 
[ 8, 5, 4 ] 
[ 5, 4, 8 ] 
[ 1, 3, 4 ] - [ 1, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(1 0 0 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1442    permutation [ 3, 1, 6, 7, 5, 4, 2, 8 ]
vertex  2 -> Algebra 1297    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1469    permutation [ 1, 5, 2, 8, 3, 7, 6, 4 ]
vertex  4 -> Algebra  842    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1483    permutation [ 1, 3, 2, 8, 4, 7, 6, 5 ]
vertex  6 -> Algebra 1346    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1071    permutation [ 3, 4, 1, 6, 7, 5, 2, 8 ]

Algebra 1345

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 1 ], [ 4, 3 ], [ 4, 5 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 8, 4, 1 ] 
[ 8, 4, 1, 2 ] 
[ 8, 4, 3 ] 
[ 1, 2, 8, 4 ] 
[ 3, 8, 4 ] 
[ 4, 1, 2, 8 ] - [ 4, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 1 1 0 0 1)
(0 0 1 0 0 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra  845    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1038    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1452    permutation [ 3, 4, 8, 6, 7, 5, 2, 1 ]
vertex  5 -> Algebra  855    permutation [ 4, 1, 2, 8, 5, 6, 7, 3 ]
vertex  6 -> Algebra  846    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1340    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 1346

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 4, 1 ] 
[ 5, 4, 1 ] 
[ 4, 1, 3 ] 
[ 8, 5, 4 ] 
[ 5, 4, 8 ] 
[ 1, 3, 4 ] - [ 1, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(1 0 0 1 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1396    permutation [ 3, 1, 5, 7, 8, 4, 2, 6 ]
vertex  2 -> Algebra 1302    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1046    permutation [ 1, 5, 2, 8, 3, 6, 7, 4 ]
vertex  4 -> Algebra  845    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1062    permutation [ 1, 3, 2, 8, 4, 6, 7, 5 ]
vertex  6 -> Algebra  847    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1341    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra 1097    permutation [ 3, 4, 1, 6, 7, 5, 2, 8 ]

Algebra 1347

Quiver

[ 1, 2 ], [ 1, 4 ], [ 2, 8 ], [ 3, 4 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 2, 8, 1 ] 
[ 4, 8, 1 ] 
[ 8, 1, 2 ] 
[ 4, 8, 5 ] 
[ 5, 4, 8 ] 
[ 8, 1, 4 ] - [ 8, 5, 4 ] 
[ 1, 2, 8 ] - [ 1, 4, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 0 0 1 1 0 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 1)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  895    permutation [ 3, 4, 8, 7, 6, 1, 2, 5 ]
vertex  2 -> Algebra 1039    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1487    permutation [ 3, 4, 8, 7, 6, 1, 2, 5 ]
vertex  4 -> Algebra  846    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1452    permutation [ 3, 4, 8, 6, 7, 5, 2, 1 ]
vertex  7 -> Algebra  848    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1348

Quiver

[ 1, 5 ], [ 2, 4 ], [ 3, 1 ], [ 4, 3 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 5, 4, 3, 1 ] 
[ 1, 5, 4, 3 ] 
[ 3, 1, 5, 4 ] 
[ 8, 5, 4 ] 
[ 5, 4, 8 ] 
[ 4, 3, 1, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(1 1 1 1 1 1 0 1)
(1 0 1 0 1 1 0 0)
(1 0 1 1 1 1 0 1)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1488    permutation [ 1, 3, 8, 7, 6, 4, 2, 5 ]
vertex  2 -> Algebra 1303    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  3 -> Algebra  847    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  948    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1547    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1046    permutation [ 1, 5, 2, 8, 3, 6, 7, 4 ]
vertex  7 -> Algebra  850    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1350

Quiver

[ 1, 2 ], [ 1, 4 ], [ 2, 8 ], [ 4, 3 ], [ 4, 8 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 1 ], [ 8, 5 ]

Relations

[ 2, 8, 1 ] 
[ 4, 8, 1 ] 
[ 8, 1, 2 ] 
[ 4, 8, 5 ] 
[ 5, 4, 8 ] 
[ 8, 1, 4 ] - [ 8, 5, 4 ] 
[ 1, 2, 8 ] - [ 1, 4, 8 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 0 0 1 1 1 1)
(0 0 1 0 0 0 0 0)
(0 0 1 1 0 0 0 1)
(0 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1095    permutation [ 3, 4, 8, 6, 7, 1, 2, 5 ]
vertex  2 -> Algebra 1040    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  848    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1487    permutation [ 3, 4, 8, 7, 6, 1, 2, 5 ]

Algebra 1351

Quiver

[ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 3 ], [ 4, 8 ], [ 5, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 3, 5, 1 ] 
[ 3, 5, 4 ] 
[ 8, 5, 4 ] 
[ 1, 3, 5 ] 
[ 5, 4, 8 ] 
[ 5, 1, 3 ] - [ 5, 4, 3 ] 
[ 4, 3, 5 ] - [ 4, 8, 5 ] 

Cartan matrix

(1 0 1 0 0 0 0 0)
(0 1 1 1 1 1 1 1)
(0 0 1 0 1 1 1 0)
(0 0 1 1 1 1 1 1)
(1 0 1 1 1 1 1 0)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra  850    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1096    permutation [ 1, 3, 8, 6, 7, 4, 2, 5 ]
vertex  3 -> Algebra 1095    permutation [ 1, 3, 8, 6, 7, 4, 2, 5 ]
vertex  5 -> Algebra 1402    permutation [ 1, 8, 3, 7, 5, 2, 4, 6 ]
vertex  7 -> Algebra 1488    permutation [ 1, 3, 8, 7, 6, 4, 2, 5 ]
vertex  8 -> Algebra 1240    permutation [ 4, 1, 3, 5, 6, 7, 2, 8 ]

Algebra 1352

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 4 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 1, 4, 3 ] 
[ 3, 1, 4 ] 
[ 5, 1, 4 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 4, 3, 1 ] - [ 4, 5, 1 ] 
[ 1, 4, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 0 1 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 0 1 0 0 1 1 0)
(1 0 1 1 1 1 1 1)
(1 0 0 0 1 1 1 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1548    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1305    permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex  5 -> Algebra  850    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1547    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1359

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 1 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ]

Relations

[ 2, 3, 4, 1 ] 
[ 8, 4, 1 ] 
[ 3, 4, 1, 2 ] 
[ 4, 1, 2, 3 ] 
[ 4, 1, 8 ] 
[ 1, 2, 3, 4 ] - [ 1, 8, 4 ] 

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(1 0 1 1 0 0 0 0)
(1 1 0 1 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 0 1 0 0 0 1)

Good mutations

vertex  1 -> Algebra 1378    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]
vertex  2 -> Algebra 1044    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1181    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1340    permutation [ 2, 3, 8, 1, 5, 7, 6, 4 ]
vertex  6 -> Algebra 1493    permutation [ 8, 4, 6, 7, 5, 1, 3, 2 ]
vertex  7 -> Algebra  855    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1362

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 1 ], [ 4, 2 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 8, 4, 1 ] 
[ 3, 4, 2 ] 
[ 8, 4, 2 ] 
[ 4, 2, 3 ] 
[ 1, 8, 4 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 
[ 4, 1, 8 ] - [ 4, 2, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 1)
(0 1 1 1 1 0 0 1)
(1 0 1 1 0 0 0 0)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(1 0 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1368    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]
vertex  2 -> Algebra 1475    permutation [ 5, 8, 1, 7, 4, 2, 3, 6 ]
vertex  3 -> Algebra 1183    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1452    permutation [ 5, 8, 4, 6, 7, 1, 3, 2 ]
vertex  6 -> Algebra 1487    permutation [ 5, 8, 4, 7, 6, 2, 3, 1 ]
vertex  7 -> Algebra 1501    permutation [ 8, 5, 4, 7, 6, 1, 3, 2 ]

Algebra 1368

Quiver

[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 1, 8, 4, 2 ] 
[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 1, 8, 6 ] 
[ 4, 2, 1, 8 ] 
[ 6, 1, 8 ] 
[ 8, 4, 2, 1 ] - [ 8, 6, 1 ] 
[ 2, 1, 8, 4 ] - [ 2, 3, 4 ] 

Cartan matrix

(1 0 0 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(1 1 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1051    permutation [ 5, 1, 8, 7, 4, 2, 3, 6 ]
vertex  4 -> Algebra 1149    permutation [ 1, 5, 8, 6, 7, 4, 3, 2 ]
vertex  5 -> Algebra 1379    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  7 -> Algebra 1502    permutation [ 1, 5, 8, 7, 6, 4, 3, 2 ]
vertex  8 -> Algebra 1362    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]

Algebra 1378

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 1 ], [ 5, 2 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 8, 5, 1 ] 
[ 3, 4, 2 ] 
[ 4, 2, 3 ] 
[ 1, 8, 5 ] 
[ 2, 8, 5 ] 
[ 4, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 5, 2 ] 
[ 2, 3, 4 ] - [ 2, 8, 4 ] 
[ 5, 1, 8 ] - [ 5, 2, 8 ] 

Cartan matrix

(1 0 0 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1405    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  4 -> Algebra 1077    permutation [ 1, 8, 5, 7, 6, 4, 3, 2 ]
vertex  5 -> Algebra 1451    permutation [ 1, 5, 8, 7, 6, 4, 3, 2 ]
vertex  6 -> Algebra 1492    permutation [ 1, 8, 6, 7, 5, 4, 3, 2 ]
vertex  7 -> Algebra  865    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1359    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]

Algebra 1379

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 3, 4, 2 ] 
[ 5, 8, 4, 2 ] 
[ 4, 2, 3 ] 
[ 5, 8, 6 ] 
[ 4, 2, 5, 8 ] 
[ 6, 5, 8 ] 
[ 2, 3, 4 ] - [ 2, 5, 8, 4 ] 
[ 8, 4, 2, 5 ] - [ 8, 6, 5 ] 

Cartan matrix

(1 0 0 1 1 0 0 1)
(0 1 1 1 1 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 1 0 0 0)
(0 0 0 1 1 0 0 1)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1368    permutation [ 5, 2, 3, 4, 1, 6, 7, 8 ]
vertex  2 -> Algebra  874    permutation [ 1, 5, 8, 7, 4, 2, 3, 6 ]
vertex  4 -> Algebra  976    permutation [ 1, 5, 8, 6, 7, 4, 3, 2 ]
vertex  5 -> Algebra  865    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1451    permutation [ 1, 5, 8, 7, 6, 4, 3, 2 ]
vertex  8 -> Algebra 1452    permutation [ 1, 5, 4, 6, 7, 8, 3, 2 ]

Algebra 1382

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 5 ], [ 3, 8 ], [ 4, 1 ], [ 5, 1 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 5, 1 ] 
[ 5, 1, 2 ] 
[ 1, 8, 4 ] 
[ 4, 1, 8 ] 
[ 5, 1, 8 ] 
[ 8, 4, 1 ] - [ 8, 5, 1 ] 
[ 1, 2, 5 ] - [ 1, 8, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 1)
(0 1 0 0 1 0 0 0)
(1 0 1 1 1 0 0 1)
(1 1 0 1 0 0 0 0)
(1 0 0 0 1 0 0 0)
(1 1 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1388    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]
vertex  2 -> Algebra 1046    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1478    permutation [ 2, 5, 1, 7, 4, 8, 3, 6 ]
vertex  4 -> Algebra 1228    permutation [ 8, 2, 5, 6, 7, 1, 3, 4 ]
vertex  5 -> Algebra 1475    permutation [ 2, 5, 1, 7, 4, 8, 3, 6 ]
vertex  6 -> Algebra 1488    permutation [ 2, 5, 4, 7, 6, 8, 3, 1 ]
vertex  7 -> Algebra 1512    permutation [ 8, 2, 5, 7, 6, 1, 3, 4 ]

Algebra 1388

Quiver

[ 1, 8 ], [ 2, 8 ], [ 3, 1 ], [ 4, 2 ], [ 6, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 4 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 8, 6, 1 ] 
[ 2, 8, 4 ] 
[ 1, 8, 6 ] 
[ 2, 8, 6 ] 
[ 4, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 6, 2 ] 
[ 6, 1, 8 ] - [ 6, 2, 8 ] 

Cartan matrix

(1 0 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1397    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1476    permutation [ 2, 8, 5, 7, 4, 1, 3, 6 ]
vertex  4 -> Algebra 1517    permutation [ 1, 2, 4, 6, 7, 5, 3, 8 ]
vertex  5 -> Algebra 1474    permutation [ 2, 8, 5, 7, 4, 1, 3, 6 ]
vertex  6 -> Algebra 1532    permutation [ 2, 8, 4, 5, 6, 3, 1, 7 ]
vertex  7 -> Algebra 1559    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1382    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]

Algebra 1393

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 7 ], [ 3, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 7, 6, 2 ] 
[ 2, 5, 3 ] 
[ 3, 2, 5 ] 
[ 6, 2, 5 ] 
[ 6, 2, 7 ] 
[ 5, 3, 2 ] - [ 5, 6, 2 ] 
[ 2, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 1 0 0 1 1 1 0)
(0 1 0 0 1 1 1 0)
(0 1 1 0 0 0 1 0)
(0 0 0 1 0 0 0 0)
(0 1 1 0 1 1 0 0)
(0 1 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1473    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1009    permutation [ 6, 2, 1, 7, 3, 8, 4, 5 ]
vertex  4 -> Algebra 1449    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  5 -> Algebra 1177    permutation [ 6, 1, 2, 5, 8, 4, 3, 7 ]
vertex  6 -> Algebra  876    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1176    permutation [ 6, 1, 2, 5, 8, 4, 3, 7 ]
vertex  8 -> Algebra  893    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1395

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 1 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 6, 2 ], [ 7, 6 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 3, 2, 1 ] 
[ 6, 2, 1 ] 
[ 8, 6, 2 ] 
[ 2, 1, 3 ] 
[ 6, 2, 8 ] 
[ 1, 3, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 0 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1407    permutation [ 6, 3, 7, 5, 1, 8, 4, 2 ]
vertex  2 -> Algebra  874    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1062    permutation [ 3, 1, 7, 5, 6, 8, 4, 2 ]
vertex  4 -> Algebra 1530    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1406    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra  885    permutation [ 1, 3, 7, 5, 6, 8, 4, 2 ]
vertex  7 -> Algebra  875    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1396

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 6, 5, 3, 2 ] 
[ 2, 6, 5, 3 ] 
[ 3, 2, 6, 5 ] 
[ 5, 3, 2, 6 ] 

Cartan matrix

(1 1 0 0 1 1 0 0)
(0 1 0 0 1 1 0 0)
(0 1 1 0 0 1 0 0)
(0 0 0 1 0 0 0 0)
(0 1 1 0 1 0 0 0)
(0 0 1 0 1 1 0 0)
(0 0 1 0 1 1 1 0)
(0 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1475    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1346    permutation [ 2, 7, 1, 6, 3, 8, 4, 5 ]
vertex  3 -> Algebra  874    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1442    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1452    permutation [ 1, 2, 5, 8, 4, 3, 7, 6 ]
vertex  7 -> Algebra  876    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  895    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1397

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 1 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 2, 8, 6, 1 ] 
[ 8, 6, 1, 2 ] 
[ 1, 2, 8, 6 ] 
[ 6, 1, 2, 8 ] 

Cartan matrix

(1 1 0 1 1 0 0 1)
(0 1 0 1 1 1 1 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra  875    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1052    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1562    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1531    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1407    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1563    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1407    permutation [ 6, 3, 7, 5, 1, 8, 4, 2 ]
vertex  8 -> Algebra 1388    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1398

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 5 ], [ 2, 8 ], [ 3, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 6, 2, 3, 1 ] 
[ 3, 1, 6, 2 ] 
[ 8, 6, 2 ] 
[ 1, 6, 2, 3 ] 
[ 6, 2, 8 ] 
[ 2, 3, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 0 0 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 0 1 0 0 1 1 0)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1476    permutation [ 3, 6, 7, 5, 1, 8, 4, 2 ]
vertex  2 -> Algebra 1302    permutation [ 3, 6, 1, 7, 2, 8, 4, 5 ]
vertex  3 -> Algebra  875    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1517    permutation [ 8, 3, 1, 2, 5, 7, 4, 6 ]
vertex  5 -> Algebra 1408    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1087    permutation [ 3, 1, 2, 5, 7, 8, 4, 6 ]
vertex  7 -> Algebra 1062    permutation [ 3, 1, 7, 5, 6, 8, 4, 2 ]

Algebra 1402

Quiver

[ 1, 5 ], [ 2, 1 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 5, 2, 1 ] 
[ 1, 5, 2 ] 
[ 8, 5, 2 ] 
[ 8, 5, 3 ] 
[ 3, 8, 5 ] 
[ 2, 1, 5 ] - [ 2, 8, 5 ] 
[ 5, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 0 1 0 1 0 0 0)
(1 1 0 1 1 0 0 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 1 0 1 1)
(0 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1548    permutation [ 5, 6, 3, 7, 1, 8, 4, 2 ]
vertex  2 -> Algebra  880    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1090    permutation [ 1, 5, 2, 8, 4, 7, 6, 3 ]
vertex  4 -> Algebra 1485    permutation [ 1, 5, 2, 4, 8, 7, 6, 3 ]
vertex  5 -> Algebra 1351    permutation [ 1, 6, 3, 7, 5, 8, 4, 2 ]
vertex  6 -> Algebra 1091    permutation [ 1, 5, 2, 8, 4, 7, 6, 3 ]

Algebra 1405

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 5, 1 ], [ 5, 3 ], [ 5, 6 ], [ 7, 6 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 5, 1 ] 
[ 8, 5, 1, 2 ] 
[ 8, 5, 3 ] 
[ 1, 2, 8, 5 ] 
[ 3, 8, 5 ] 
[ 5, 1, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 1 0 1 0 0 0 1)
(0 1 0 1 1 1 0 1)
(0 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(1 1 1 1 1 1 0 1)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 0 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra  884    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1061    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1489    permutation [ 1, 2, 4, 7, 6, 8, 3, 5 ]
vertex  5 -> Algebra 1530    permutation [ 1, 8, 6, 2, 4, 5, 3, 7 ]
vertex  6 -> Algebra 1428    permutation [ 5, 1, 2, 8, 4, 6, 7, 3 ]
vertex  7 -> Algebra  885    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1378    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1406

Quiver

[ 1, 3 ], [ 1, 6 ], [ 2, 5 ], [ 3, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 3, 5, 1 ] 
[ 6, 5, 1 ] 
[ 5, 1, 3 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 1, 3, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 1 0 1 1 0 0)
(1 1 0 1 1 1 0 1)
(0 0 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 1 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1535    permutation [ 6, 3, 5, 7, 1, 8, 4, 2 ]
vertex  2 -> Algebra 1395    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1461    permutation [ 3, 1, 5, 7, 6, 8, 4, 2 ]
vertex  4 -> Algebra 1534    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra  884    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1307    permutation [ 1, 3, 5, 7, 6, 8, 4, 2 ]
vertex  7 -> Algebra  886    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1407

Quiver

[ 1, 5 ], [ 2, 5 ], [ 3, 1 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 5, 8, 6, 1 ] 
[ 8, 6, 1, 5 ] 
[ 1, 5, 8, 6 ] 
[ 6, 1, 5, 8 ] 

Cartan matrix

(1 0 0 1 1 0 0 1)
(0 1 0 1 1 1 1 1)
(1 0 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(0 0 0 1 1 1 1 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra  886    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1397    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1397    permutation [ 5, 8, 2, 7, 4, 1, 3, 6 ]
vertex  4 -> Algebra 1535    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1395    permutation [ 5, 8, 2, 7, 4, 1, 3, 6 ]
vertex  6 -> Algebra 1559    permutation [ 5, 6, 2, 7, 4, 1, 3, 8 ]
vertex  7 -> Algebra 1535    permutation [ 6, 3, 5, 7, 1, 8, 4, 2 ]
vertex  8 -> Algebra 1474    permutation [ 8, 5, 2, 7, 4, 1, 3, 6 ]

Algebra 1408

Quiver

[ 1, 6 ], [ 2, 5 ], [ 3, 1 ], [ 5, 3 ], [ 5, 8 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 6, 5, 3, 1 ] 
[ 1, 6, 5, 3 ] 
[ 3, 1, 6, 5 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 5, 3, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 0 0 1 1 1 0)
(1 1 1 1 1 1 1 1)
(1 0 1 0 0 1 1 0)
(0 0 0 1 0 0 0 0)
(1 0 1 1 1 1 1 1)
(0 0 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(0 0 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1563    permutation [ 5, 8, 2, 7, 4, 3, 1, 6 ]
vertex  2 -> Algebra 1398    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra  886    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1447    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  5 -> Algebra  912    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1128    permutation [ 3, 1, 2, 5, 7, 8, 4, 6 ]
vertex  7 -> Algebra 1461    permutation [ 3, 1, 5, 7, 6, 8, 4, 2 ]

Algebra 1412

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 1 ], [ 6, 1 ], [ 6, 7 ], [ 8, 5 ]

Relations

[ 2, 3, 5, 1 ] 
[ 8, 5, 1 ] 
[ 3, 5, 1, 2 ] 
[ 5, 1, 2, 3 ] 
[ 5, 1, 8 ] 
[ 1, 2, 3, 5 ] - [ 1, 8, 5 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(0 1 1 0 1 0 0 0)
(1 0 1 0 1 0 0 0)
(1 1 0 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(1 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1416    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]
vertex  2 -> Algebra 1064    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1199    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1428    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra 1478    permutation [ 2, 3, 1, 7, 4, 5, 8, 6 ]
vertex  6 -> Algebra 1489    permutation [ 2, 3, 4, 7, 6, 5, 8, 1 ]
vertex  7 -> Algebra 1566    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1416

Quiver

[ 1, 8 ], [ 2, 3 ], [ 2, 8 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 6, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 8, 6, 1 ] 
[ 3, 5, 2 ] 
[ 5, 2, 3 ] 
[ 1, 8, 6 ] 
[ 2, 8, 6 ] 
[ 5, 2, 8 ] 
[ 8, 5, 2 ] - [ 8, 6, 2 ] 
[ 2, 3, 5 ] - [ 2, 8, 5 ] 
[ 6, 1, 8 ] - [ 6, 2, 8 ] 

Cartan matrix

(1 0 0 0 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 1 0 1 0 0 0)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(1 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1303    permutation [ 8, 6, 1, 7, 2, 5, 4, 3 ]
vertex  4 -> Algebra 1305    permutation [ 8, 6, 1, 7, 2, 5, 4, 3 ]
vertex  5 -> Algebra 1560    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1568    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1547    permutation [ 8, 7, 1, 6, 2, 5, 4, 3 ]
vertex  8 -> Algebra 1412    permutation [ 8, 2, 3, 4, 5, 6, 7, 1 ]

Algebra 1428

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 5 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ]

Relations

[ 2, 3, 4, 1 ] 
[ 8, 4, 1 ] 
[ 3, 4, 1, 2 ] 
[ 4, 1, 2, 3 ] 
[ 4, 1, 8 ] 
[ 1, 2, 3, 4 ] - [ 1, 8, 4 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 1 1 1 0 0 0)
(1 0 1 1 1 0 0 0)
(1 1 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 1 1 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 0 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1305    permutation [ 1, 6, 8, 7, 2, 4, 5, 3 ]
vertex  2 -> Algebra 1091    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1222    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1492    permutation [ 2, 3, 6, 7, 1, 5, 8, 4 ]
vertex  5 -> Algebra 1412    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1405    permutation [ 2, 3, 8, 5, 1, 6, 7, 4 ]
vertex  7 -> Algebra 1548    permutation [ 1, 7, 8, 6, 2, 4, 5, 3 ]

Algebra 1442

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 8 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 6, 8, 5, 2 ] 
[ 2, 6, 8, 5 ] 
[ 8, 5, 2, 6 ] 
[ 5, 2, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 1)
(0 1 0 0 0 1 0 1)
(0 1 1 1 1 1 0 0)
(0 1 0 1 1 1 0 0)
(0 1 0 0 1 1 0 0)
(0 0 0 0 1 1 0 1)
(0 0 0 0 1 1 1 1)
(0 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1495    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1341    permutation [ 2, 7, 1, 6, 5, 3, 4, 8 ]
vertex  3 -> Algebra 1396    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  5 -> Algebra 1291    permutation [ 1, 2, 4, 5, 8, 6, 7, 3 ]
vertex  6 -> Algebra 1450    permutation [ 1, 2, 8, 3, 4, 5, 7, 6 ]
vertex  7 -> Algebra  958    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1447

Quiver

[ 1, 6 ], [ 2, 8 ], [ 3, 4 ], [ 4, 6 ], [ 5, 1 ], [ 6, 7 ], [ 6, 8 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 6, 8, 5, 1 ] 
[ 6, 8, 4 ] 
[ 1, 6, 8, 5 ] 
[ 4, 6, 8 ] 
[ 5, 1, 6, 8 ] 
[ 8, 4, 6 ] - [ 8, 5, 1, 6 ] 

Cartan matrix

(1 0 0 0 0 1 1 1)
(1 1 0 1 1 1 1 1)
(0 0 1 1 0 1 1 0)
(0 0 0 1 0 1 1 0)
(1 0 0 0 1 1 1 0)
(0 0 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 0 1 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1559    permutation [ 4, 5, 3, 1, 7, 8, 2, 6 ]
vertex  2 -> Algebra 1517    permutation [ 4, 5, 1, 8, 2, 7, 3, 6 ]
vertex  3 -> Algebra 1408    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  5 -> Algebra 1308    permutation [ 1, 2, 4, 5, 8, 6, 7, 3 ]
vertex  6 -> Algebra 1200    permutation [ 4, 5, 1, 2, 8, 7, 3, 6 ]
vertex  7 -> Algebra 1486    permutation [ 1, 6, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra  955    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1449

Quiver

[ 1, 2 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 7, 6 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 7, 6, 2 ] 
[ 2, 8, 5 ] 
[ 6, 2, 7 ] 
[ 5, 2, 8 ] 
[ 6, 2, 8 ] 
[ 8, 5, 2 ] - [ 8, 6, 2 ] 
[ 2, 7, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 0 0 0 1 1 1)
(0 1 0 0 0 1 1 1)
(0 1 1 1 1 0 1 0)
(0 1 0 1 1 0 1 0)
(0 1 0 0 1 0 1 0)
(0 1 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1500    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1005    permutation [ 6, 2, 1, 7, 5, 3, 4, 8 ]
vertex  3 -> Algebra 1393    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  6 -> Algebra  958    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1172    permutation [ 6, 1, 2, 8, 3, 4, 5, 7 ]
vertex  8 -> Algebra 1173    permutation [ 6, 1, 2, 8, 3, 4, 5, 7 ]

Algebra 1450

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 2 ], [ 7, 3 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 6, 2, 3 ] 
[ 2, 3, 6 ] 
[ 3, 8, 7 ] 
[ 2, 3, 8 ] 
[ 7, 3, 8 ] 
[ 3, 6, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 7, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 1 1 0 0 1 0 1)
(0 1 0 1 1 1 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 0 0 1 0 0)
(0 0 1 0 0 1 1 0)
(0 1 1 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1501    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1340    permutation [ 8, 7, 1, 2, 6, 4, 5, 3 ]
vertex  4 -> Algebra 1452    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1451    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1172    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1442    permutation [ 1, 2, 4, 5, 6, 8, 7, 3 ]

Algebra 1451

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 2 ], [ 6, 8 ], [ 7, 6 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 5, 2, 3 ] 
[ 6, 8, 2, 3 ] 
[ 2, 3, 5 ] 
[ 6, 8, 7 ] 
[ 2, 3, 6, 8 ] 
[ 7, 6, 8 ] 
[ 3, 5, 2 ] - [ 3, 6, 8, 2 ] 
[ 8, 2, 3, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 1 1 0 0 1 0 0)
(0 1 1 0 0 1 0 0)
(0 1 1 0 1 1 0 1)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1502    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1378    permutation [ 1, 8, 7, 6, 2, 5, 4, 3 ]
vertex  3 -> Algebra 1450    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra 1379    permutation [ 1, 8, 7, 6, 2, 5, 4, 3 ]
vertex  6 -> Algebra  964    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1291    permutation [ 1, 2, 5, 3, 6, 8, 7, 4 ]

Algebra 1452

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 6, 2 ], [ 7, 3 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 6, 2, 3 ] 
[ 2, 3, 6 ] 
[ 3, 8, 7 ] 
[ 2, 3, 8 ] 
[ 7, 3, 8 ] 
[ 3, 6, 2 ] - [ 3, 8, 2 ] 
[ 8, 2, 3 ] - [ 8, 7, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 1 1 0 0 1 0 1)
(0 1 0 1 1 1 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 0 1 0 0)
(0 0 1 0 0 1 1 0)
(0 1 1 0 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1362    permutation [ 6, 8, 7, 3, 1, 4, 5, 2 ]
vertex  2 -> Algebra 1345    permutation [ 8, 7, 1, 2, 6, 4, 5, 3 ]
vertex  4 -> Algebra 1347    permutation [ 8, 7, 1, 2, 6, 4, 5, 3 ]
vertex  5 -> Algebra 1450    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  6 -> Algebra 1379    permutation [ 1, 8, 7, 3, 2, 4, 5, 6 ]
vertex  7 -> Algebra 1176    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1396    permutation [ 1, 2, 6, 5, 3, 8, 7, 4 ]

Algebra 1455

Quiver

[ 2, 1 ], [ 2, 4 ], [ 2, 6 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 2 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 6, 5, 2 ] 
[ 2, 4, 3 ] 
[ 3, 2, 4 ] 
[ 5, 2, 4 ] 
[ 5, 2, 6 ] 
[ 4, 3, 2 ] - [ 4, 5, 2 ] 
[ 2, 4, 5 ] - [ 2, 6, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 1 1 1 0 0)
(1 1 1 0 0 1 0 0)
(1 1 1 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1291    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1569    permutation [ 2, 5, 8, 7, 6, 1, 4, 3 ]
vertex  4 -> Algebra 1495    permutation [ 1, 2, 8, 3, 4, 6, 7, 5 ]
vertex  5 -> Algebra 1010    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1502    permutation [ 2, 1, 4, 8, 3, 5, 7, 6 ]
vertex  7 -> Algebra 1001    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1051    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1456

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 1 ], [ 3, 6 ], [ 4, 2 ], [ 5, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 1, 2 ] 
[ 1, 2, 3 ] 
[ 6, 2, 3 ] 
[ 1, 2, 5 ] 
[ 2, 3, 6 ] 
[ 2, 3, 1 ] - [ 2, 5, 1 ] 
[ 3, 1, 2 ] - [ 3, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 1 0 1 0 0 0)
(1 1 1 0 0 1 1 0)
(1 1 1 1 1 0 0 0)
(1 0 0 0 1 0 0 0)
(0 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1531    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1001    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1563    permutation [ 3, 6, 8, 4, 7, 1, 5, 2 ]
vertex  5 -> Algebra 1461    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1570    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1569    permutation [ 2, 5, 8, 7, 6, 1, 4, 3 ]
vertex  8 -> Algebra 1052    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1457

Quiver

[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]

Relations

[ 5, 4, 3, 2 ] 
[ 2, 5, 4, 3 ] 
[ 3, 2, 5, 4 ] 
[ 4, 3, 2, 5 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 1 1 0 0 0)
(1 1 1 0 1 0 0 0)
(1 1 1 1 0 0 0 0)
(0 0 1 1 1 0 0 0)
(0 0 1 1 1 1 1 0)
(0 0 1 1 1 0 1 0)
(1 1 1 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1298    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1508    permutation [ 5, 1, 2, 8, 3, 7, 6, 4 ]
vertex  3 -> Algebra 1005    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1259    permutation [ 7, 2, 1, 4, 8, 3, 6, 5 ]
vertex  6 -> Algebra 1132    permutation [ 2, 1, 5, 8, 3, 7, 6, 4 ]
vertex  8 -> Algebra 1057    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1460

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 3, 5, 4 ] 
[ 2, 3, 5 ] 
[ 4, 3, 5 ] 
[ 3, 1, 2 ] - [ 3, 5, 2 ] 
[ 5, 2, 3 ] - [ 5, 4, 3 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(1 1 1 0 1 1 0 0)
(1 0 1 1 0 0 0 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1489    permutation [ 2, 1, 8, 7, 6, 3, 4, 5 ]
vertex  2 -> Algebra 1010    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1067    permutation [ 2, 3, 8, 7, 6, 1, 4, 5 ]
vertex  4 -> Algebra 1125    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  5 -> Algebra 1486    permutation [ 2, 5, 8, 7, 6, 1, 4, 3 ]
vertex  6 -> Algebra 1199    permutation [ 5, 1, 2, 8, 3, 6, 7, 4 ]
vertex  7 -> Algebra 1012    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1061    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1461

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 1 ], [ 3, 6 ], [ 4, 5 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 2, 5, 3, 1 ] 
[ 5, 3, 1, 2 ] 
[ 1, 2, 5, 3 ] 
[ 6, 5, 3 ] 
[ 5, 3, 6 ] 
[ 3, 1, 2, 5 ] - [ 3, 6, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 1 0 1 0 0 0)
(1 1 1 0 1 1 1 0)
(1 0 1 1 1 0 0 0)
(1 0 1 0 1 0 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1406    permutation [ 2, 8, 1, 7, 3, 5, 4, 6 ]
vertex  2 -> Algebra 1456    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1092    permutation [ 2, 5, 8, 6, 7, 1, 4, 3 ]
vertex  4 -> Algebra 1408    permutation [ 2, 8, 1, 7, 3, 5, 4, 6 ]
vertex  5 -> Algebra 1012    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1486    permutation [ 2, 5, 8, 7, 6, 1, 4, 3 ]
vertex  8 -> Algebra 1062    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1469

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 6, 2 ], [ 7, 6 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 5, 1 ] 
[ 2, 8, 4 ] 
[ 1, 2, 8, 5 ] 
[ 4, 2, 8 ] 
[ 5, 1, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 5, 1, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 0 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(1 1 0 0 1 0 0 0)
(0 1 0 0 1 1 0 1)
(0 1 0 0 1 1 1 1)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1512    permutation [ 8, 1, 5, 7, 6, 2, 3, 4 ]
vertex  2 -> Algebra 1474    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1532    permutation [ 1, 8, 5, 3, 2, 7, 6, 4 ]
vertex  5 -> Algebra 1341    permutation [ 1, 3, 5, 8, 2, 7, 6, 4 ]
vertex  7 -> Algebra 1046    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1045    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1470

Quiver

[ 1, 2 ], [ 2, 8 ], [ 4, 2 ], [ 5, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 5, 1 ] 
[ 2, 8, 4 ] 
[ 1, 2, 8, 5 ] 
[ 4, 2, 8 ] 
[ 5, 1, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 5, 1, 2 ] 

Cartan matrix

(1 1 1 0 0 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 1 0 0 0 0 0)
(0 1 0 1 0 0 0 0)
(1 1 0 0 1 0 0 0)
(0 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 1 1 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1478    permutation [ 1, 5, 2, 7, 4, 8, 3, 6 ]
vertex  2 -> Algebra 1476    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1046    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1302    permutation [ 1, 8, 5, 3, 2, 6, 7, 4 ]
vertex  6 -> Algebra 1303    permutation [ 1, 8, 5, 3, 2, 6, 7, 4 ]
vertex  7 -> Algebra 1532    permutation [ 1, 8, 5, 3, 2, 7, 6, 4 ]
vertex  8 -> Algebra 1064    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1473

Quiver

[ 2, 1 ], [ 2, 5 ], [ 2, 7 ], [ 3, 2 ], [ 5, 3 ], [ 5, 6 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 7, 6, 2 ] 
[ 2, 5, 3 ] 
[ 3, 2, 5 ] 
[ 6, 2, 5 ] 
[ 6, 2, 7 ] 
[ 5, 3, 2 ] - [ 5, 6, 2 ] 
[ 2, 5, 6 ] - [ 2, 7, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 0 1 1 1 0)
(1 1 1 0 0 0 1 0)
(0 0 0 1 0 0 0 0)
(1 1 1 0 1 1 0 0)
(1 1 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 1 0 0 1 1)

Good mutations

vertex  1 -> Algebra 1393    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1199    permutation [ 3, 6, 1, 5, 2, 8, 4, 7 ]
vertex  4 -> Algebra 1500    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  5 -> Algebra 1267    permutation [ 6, 2, 1, 5, 8, 4, 3, 7 ]
vertex  6 -> Algebra 1053    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1183    permutation [ 3, 6, 7, 5, 1, 8, 4, 2 ]
vertex  8 -> Algebra 1067    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1474

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 8 ], [ 3, 2 ], [ 5, 1 ], [ 6, 2 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 5, 1, 2 ] 
[ 1, 2, 5 ] 
[ 2, 8, 6 ] 
[ 1, 2, 8 ] 
[ 6, 2, 8 ] 
[ 2, 5, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(1 1 0 1 1 0 0 1)
(1 1 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 0 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(1 1 0 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1407    permutation [ 6, 3, 7, 5, 2, 8, 4, 1 ]
vertex  2 -> Algebra 1051    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1388    permutation [ 6, 1, 7, 5, 3, 8, 4, 2 ]
vertex  4 -> Algebra 1569    permutation [ 2, 5, 4, 7, 6, 1, 3, 8 ]
vertex  5 -> Algebra 1483    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  7 -> Algebra 1052    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1469    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1475

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 6, 5, 3, 2 ] 
[ 2, 6, 5, 3 ] 
[ 3, 2, 6, 5 ] 
[ 5, 3, 2, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 0 1 1 0 0)
(1 1 1 0 0 1 0 0)
(0 0 0 1 0 0 0 0)
(1 1 1 0 1 0 0 0)
(0 0 1 0 1 1 0 0)
(0 0 1 0 1 1 1 0)
(1 1 1 1 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1396    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1382    permutation [ 3, 1, 7, 5, 2, 8, 4, 6 ]
vertex  3 -> Algebra 1051    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1495    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1362    permutation [ 3, 6, 7, 5, 1, 8, 4, 2 ]
vertex  7 -> Algebra 1053    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1069    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1476

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 2, 8 ], [ 5, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 5, 1, 2 ] 
[ 1, 2, 5 ] 
[ 2, 8, 6 ] 
[ 1, 2, 8 ] 
[ 6, 2, 8 ] 
[ 2, 5, 1 ] - [ 2, 8, 1 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(1 1 1 1 1 0 0 1)
(0 0 1 0 0 0 0 0)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1562    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1478    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1052    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1563    permutation [ 8, 6, 4, 3, 7, 1, 5, 2 ]
vertex  5 -> Algebra 1398    permutation [ 5, 8, 1, 7, 4, 2, 3, 6 ]
vertex  6 -> Algebra 1560    permutation [ 7, 1, 6, 5, 3, 8, 4, 2 ]
vertex  7 -> Algebra 1388    permutation [ 6, 1, 7, 5, 3, 8, 4, 2 ]
vertex  8 -> Algebra 1470    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1477

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 6 ], [ 3, 2 ], [ 5, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 5, 1, 2 ] 
[ 6, 8, 1, 2 ] 
[ 1, 2, 5 ] 
[ 6, 8, 7 ] 
[ 1, 2, 6, 8 ] 
[ 7, 6, 8 ] 
[ 2, 5, 1 ] - [ 2, 6, 8, 1 ] 
[ 8, 1, 2, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(1 1 0 1 1 1 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 0 1 0 0 0)
(1 0 0 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(1 1 0 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1563    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1560    permutation [ 7, 1, 6, 5, 3, 8, 4, 2 ]
vertex  4 -> Algebra 1570    permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex  6 -> Algebra 1052    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1547    permutation [ 1, 3, 5, 2, 6, 8, 7, 4 ]

Algebra 1478

Quiver

[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 5, 3 ], [ 6, 2 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ]

Relations

[ 2, 3, 1 ] 
[ 1, 2, 3 ] 
[ 3, 6, 5 ] 
[ 2, 3, 6 ] 
[ 5, 3, 6 ] 
[ 3, 1, 2 ] - [ 3, 6, 2 ] 
[ 6, 2, 3 ] - [ 6, 5, 3 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(1 1 1 0 0 1 1 0)
(0 0 0 1 0 0 0 0)
(1 0 1 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 1 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1470    permutation [ 1, 3, 7, 5, 2, 8, 4, 6 ]
vertex  2 -> Algebra 1053    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1476    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1498    permutation [ 1, 2, 4, 8, 3, 6, 7, 5 ]
vertex  5 -> Algebra 1088    permutation [ 1, 2, 8, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra 1412    permutation [ 3, 1, 2, 5, 6, 8, 4, 7 ]
vertex  7 -> Algebra 1382    permutation [ 3, 1, 7, 5, 2, 8, 4, 6 ]
vertex  8 -> Algebra 1070    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1481

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 5, 2 ], [ 5, 3 ], [ 6, 7 ], [ 7, 5 ], [ 8, 1 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 2, 8, 1 ] 
[ 8, 5, 3 ] 
[ 2, 8, 5 ] 
[ 3, 8, 5 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 5, 2 ] 
[ 5, 2, 8 ] - [ 5, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 0 0 1)
(0 1 1 1 1 1 1 1)
(0 1 1 1 1 0 1 1)
(1 1 0 1 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1548    permutation [ 5, 6, 3, 7, 2, 8, 4, 1 ]
vertex  2 -> Algebra 1057    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1221    permutation [ 5, 1, 2, 8, 4, 7, 6, 3 ]
vertex  4 -> Algebra 1508    permutation [ 5, 1, 2, 4, 8, 7, 6, 3 ]
vertex  6 -> Algebra 1222    permutation [ 5, 1, 2, 8, 4, 7, 6, 3 ]
vertex  8 -> Algebra 1327    permutation [ 1, 3, 2, 8, 6, 7, 5, 4 ]

Algebra 1483

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 5 ], [ 5, 8 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 2, 5, 8, 1 ] 
[ 5, 8, 1, 2 ] 
[ 5, 8, 6 ] 
[ 1, 2, 5, 8 ] 
[ 6, 5, 8 ] 
[ 8, 1, 2, 5 ] - [ 8, 6, 5 ] 

Cartan matrix

(1 1 0 0 1 0 0 0)
(0 1 0 1 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 0 0 1 0 0 0 0)
(1 0 0 1 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 0 1 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1530    permutation [ 2, 8, 6, 1, 4, 5, 3, 7 ]
vertex  2 -> Algebra 1474    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1517    permutation [ 6, 1, 2, 8, 4, 3, 7, 5 ]
vertex  4 -> Algebra 1486    permutation [ 2, 5, 4, 7, 6, 1, 3, 8 ]
vertex  5 -> Algebra 1061    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1062    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1341    permutation [ 1, 3, 2, 5, 8, 7, 6, 4 ]

Algebra 1485

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 2, 3, 1 ] 
[ 8, 5, 2 ] 
[ 1, 2, 3 ] 
[ 5, 2, 3 ] 
[ 5, 2, 8 ] 
[ 3, 1, 2 ] - [ 3, 5, 2 ] 
[ 2, 3, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 1 0 1 0 0 1)
(1 1 1 0 1 0 0 0)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(0 1 1 0 1 1 0 1)
(0 1 1 0 1 1 1 1)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1566    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1488    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]
vertex  3 -> Algebra 1298    permutation [ 1, 3, 5, 8, 2, 7, 6, 4 ]
vertex  4 -> Algebra 1402    permutation [ 1, 3, 8, 4, 2, 7, 6, 5 ]
vertex  5 -> Algebra 1532    permutation [ 1, 5, 3, 8, 2, 7, 6, 4 ]
vertex  7 -> Algebra 1064    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1063    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1486

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 6, 1 ], [ 7, 2 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 2, 8, 6, 1 ] 
[ 2, 8, 5 ] 
[ 1, 2, 8, 6 ] 
[ 5, 2, 8 ] 
[ 6, 1, 2, 8 ] 
[ 8, 5, 2 ] - [ 8, 6, 1, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 1)
(0 1 0 0 0 1 0 1)
(1 1 1 0 1 1 0 1)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 0 0 0)
(1 1 0 0 0 1 0 0)
(0 1 0 0 0 1 1 1)
(1 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1569    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1460    permutation [ 6, 1, 8, 7, 2, 5, 4, 3 ]
vertex  3 -> Algebra 1483    permutation [ 6, 1, 7, 3, 2, 5, 4, 8 ]
vertex  4 -> Algebra 1461    permutation [ 6, 1, 8, 7, 2, 5, 4, 3 ]
vertex  6 -> Algebra 1534    permutation [ 1, 3, 5, 6, 8, 2, 7, 4 ]
vertex  7 -> Algebra 1447    permutation [ 1, 3, 4, 5, 6, 2, 7, 8 ]
vertex  8 -> Algebra 1065    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1487

Quiver

[ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 6, 7 ], [ 7, 3 ], [ 8, 2 ], [ 8, 5 ]

Relations

[ 8, 2, 3 ] 
[ 2, 3, 6 ] 
[ 7, 3, 6 ] 
[ 3, 6, 7 ] 
[ 2, 3, 8 ] 
[ 3, 6, 2 ] - [ 3, 8, 2 ] 
[ 6, 2, 3 ] - [ 6, 7, 3 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 0 0)
(1 1 1 0 1 1 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 1 0 0 1 1 0)
(0 0 1 0 1 0 1 1)
(1 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1347    permutation [ 6, 7, 1, 2, 8, 5, 4, 3 ]
vertex  4 -> Algebra 1350    permutation [ 6, 7, 1, 2, 8, 5, 4, 3 ]
vertex  5 -> Algebra 1362    permutation [ 8, 6, 7, 3, 1, 5, 4, 2 ]
vertex  6 -> Algebra 1069    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1268    permutation [ 7, 2, 1, 3, 8, 4, 5, 6 ]

Algebra 1488

Quiver

[ 1, 2 ], [ 2, 8 ], [ 3, 8 ], [ 4, 5 ], [ 6, 2 ], [ 6, 3 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 2, 8, 1 ] 
[ 8, 6, 3 ] 
[ 2, 8, 6 ] 
[ 3, 8, 6 ] 
[ 1, 2, 8 ] 
[ 8, 1, 2 ] - [ 8, 6, 2 ] 
[ 6, 2, 8 ] - [ 6, 3, 8 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 1)
(1 0 1 0 1 0 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 0 1)
(0 1 1 0 1 1 1 1)
(1 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1348    permutation [ 1, 7, 2, 6, 8, 5, 4, 3 ]
vertex  2 -> Algebra 1069    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1232    permutation [ 6, 1, 2, 8, 4, 5, 7, 3 ]
vertex  4 -> Algebra 1351    permutation [ 1, 7, 2, 6, 8, 5, 4, 3 ]
vertex  5 -> Algebra 1382    permutation [ 8, 1, 7, 3, 2, 5, 4, 6 ]
vertex  7 -> Algebra 1070    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1485    permutation [ 1, 8, 3, 4, 5, 6, 7, 2 ]

Algebra 1489

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 6 ], [ 4, 5 ], [ 6, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ], [ 8, 7 ]

Relations

[ 2, 6, 8, 1 ] 
[ 6, 8, 1, 2 ] 
[ 6, 8, 7 ] 
[ 1, 2, 6, 8 ] 
[ 7, 6, 8 ] 
[ 8, 1, 2, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 0 0 1 1 0 1)
(1 0 1 0 1 1 0 1)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 0 0 0 1 1 0 1)
(0 0 0 0 0 1 1 0)
(1 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1304    permutation [ 1, 2, 6, 7, 8, 5, 4, 3 ]
vertex  2 -> Algebra 1460    permutation [ 2, 1, 6, 7, 8, 5, 4, 3 ]
vertex  3 -> Algebra 1405    permutation [ 1, 2, 7, 3, 8, 5, 4, 6 ]
vertex  4 -> Algebra 1307    permutation [ 1, 2, 6, 7, 8, 5, 4, 3 ]
vertex  5 -> Algebra 1412    permutation [ 8, 1, 2, 3, 6, 5, 4, 7 ]
vertex  6 -> Algebra 1070    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1534    permutation [ 1, 3, 5, 2, 6, 8, 7, 4 ]

Algebra 1492

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 8 ], [ 7, 6 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 2, 5, 1 ] 
[ 6, 8, 2 ] 
[ 1, 2, 5 ] 
[ 8, 2, 5 ] 
[ 6, 8, 7 ] 
[ 7, 6, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 7, 6 ] 
[ 2, 5, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 0 0 1 1 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 1 1 1)
(0 0 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1493    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1378    permutation [ 1, 8, 7, 6, 5, 3, 4, 2 ]
vertex  4 -> Algebra 1497    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1088    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1428    permutation [ 5, 1, 2, 8, 6, 3, 4, 7 ]

Algebra 1493

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 3, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 2 ], [ 8, 7 ]

Relations

[ 2, 6, 1 ] 
[ 1, 2, 6 ] 
[ 8, 7, 2, 6 ] 
[ 2, 6, 8, 7 ] 
[ 7, 2, 6, 8 ] 
[ 6, 1, 2 ] - [ 6, 8, 7, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 1 0 1)
(1 1 1 1 1 1 1 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 1 1 1)
(1 1 0 0 0 1 1 1)
(0 1 0 0 0 1 1 0)
(0 1 0 0 0 0 1 1)

Good mutations

vertex  3 -> Algebra 1359    permutation [ 6, 8, 7, 2, 5, 3, 4, 1 ]
vertex  4 -> Algebra 1499    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1492    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1230    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1337    permutation [ 8, 7, 1, 6, 3, 4, 5, 2 ]

Algebra 1495

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 8 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 6, 8, 5, 2 ] 
[ 2, 6, 8, 5 ] 
[ 8, 5, 2, 6 ] 
[ 5, 2, 6, 8 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 0 0 1 0 1)
(1 1 1 1 1 1 0 0)
(1 1 0 1 1 1 0 0)
(1 1 0 0 1 1 0 0)
(0 0 0 0 1 1 0 1)
(0 0 0 0 1 1 1 1)
(1 1 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1442    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1512    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  3 -> Algebra 1475    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  5 -> Algebra 1455    permutation [ 1, 2, 4, 5, 8, 6, 7, 3 ]
vertex  6 -> Algebra 1501    permutation [ 2, 1, 8, 3, 4, 5, 7, 6 ]
vertex  7 -> Algebra 1131    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1497

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 8 ], [ 7, 6 ], [ 8, 2 ], [ 8, 7 ]

Relations

[ 2, 5, 1 ] 
[ 6, 8, 2 ] 
[ 1, 2, 5 ] 
[ 8, 2, 5 ] 
[ 6, 8, 7 ] 
[ 7, 6, 8 ] 
[ 5, 1, 2 ] - [ 5, 8, 2 ] 
[ 8, 2, 6 ] - [ 8, 7, 6 ] 
[ 2, 5, 8 ] - [ 2, 6, 8 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(0 1 0 0 1 1 0 1)
(1 1 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(1 1 0 0 1 1 1 1)
(0 0 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 0 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1499    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  3 -> Algebra 1492    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1129    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1548    permutation [ 5, 3, 7, 4, 1, 8, 6, 2 ]

Algebra 1498

Quiver

[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5, 1 ], [ 5, 6 ], [ 6, 2 ], [ 6, 7 ], [ 6, 8 ], [ 8, 5 ]

Relations

[ 2, 5, 1 ] 
[ 1, 2, 5 ] 
[ 2, 5, 6 ] 
[ 8, 5, 6 ] 
[ 5, 6, 8 ] 
[ 5, 1, 2 ] - [ 5, 6, 2 ] 
[ 6, 2, 5 ] - [ 6, 8, 5 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 1 0 0 0)
(1 1 1 1 1 1 1 0)
(1 1 0 1 1 1 1 0)
(1 1 0 0 1 1 1 0)
(0 1 0 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(1 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1532    permutation [ 1, 6, 2, 7, 5, 3, 4, 8 ]
vertex  2 -> Algebra 1131    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1478    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  5 -> Algebra 1563    permutation [ 4, 6, 3, 2, 7, 1, 8, 5 ]
vertex  6 -> Algebra 1566    permutation [ 5, 1, 2, 8, 6, 4, 3, 7 ]
vertex  7 -> Algebra 1512    permutation [ 6, 1, 2, 3, 4, 5, 7, 8 ]
vertex  8 -> Algebra 1129    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1499

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 8 ], [ 7, 2 ], [ 8, 7 ]

Relations

[ 2, 6, 1 ] 
[ 1, 2, 6 ] 
[ 8, 7, 2, 6 ] 
[ 2, 6, 8, 7 ] 
[ 7, 2, 6, 8 ] 
[ 6, 1, 2 ] - [ 6, 8, 7, 2 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 0 0 0 1 0 1)
(1 1 1 1 1 1 1 1)
(1 1 0 1 1 1 1 1)
(1 1 0 0 1 1 1 1)
(1 1 0 0 0 1 1 1)
(0 1 0 0 0 1 1 0)
(0 1 0 0 0 0 1 1)

Good mutations

vertex  3 -> Algebra 1493    permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1497    permutation [ 1, 6, 3, 4, 5, 2, 7, 8 ]
vertex  7 -> Algebra 1209    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1327    permutation [ 8, 7, 1, 6, 3, 4, 5, 2 ]

Algebra 1500

Quiver

[ 2, 1 ], [ 2, 7 ], [ 2, 8 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 2 ], [ 7, 6 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 7, 6, 2 ] 
[ 2, 8, 5 ] 
[ 6, 2, 7 ] 
[ 5, 2, 8 ] 
[ 6, 2, 8 ] 
[ 8, 5, 2 ] - [ 8, 6, 2 ] 
[ 2, 7, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 0 0 0 1 1 1)
(1 1 1 1 1 0 1 0)
(1 1 0 1 1 0 1 0)
(1 1 0 0 1 0 1 0)
(1 1 0 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1449    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1508    permutation [ 5, 6, 1, 8, 2, 4, 3, 7 ]
vertex  3 -> Algebra 1473    permutation [ 1, 2, 5, 3, 8, 6, 7, 4 ]
vertex  6 -> Algebra 1131    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1262    permutation [ 6, 2, 1, 8, 3, 4, 5, 7 ]
vertex  8 -> Algebra 1263    permutation [ 6, 2, 1, 8, 3, 4, 5, 7 ]

Algebra 1501

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 7, 3 ], [ 8, 1 ], [ 8, 7 ]

Relations

[ 6, 1, 3 ] 
[ 1, 3, 6 ] 
[ 3, 8, 7 ] 
[ 1, 3, 8 ] 
[ 7, 3, 8 ] 
[ 3, 6, 1 ] - [ 3, 8, 1 ] 
[ 8, 1, 3 ] - [ 8, 7, 3 ] 

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 0 0 1 0 1)
(1 1 0 1 1 1 0 0)
(1 1 0 0 1 1 0 0)
(1 1 0 0 0 1 0 0)
(0 0 1 0 0 1 1 0)
(1 1 1 0 0 0 1 1)

Good mutations

vertex  2 -> Algebra 1450    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1362    permutation [ 6, 8, 7, 3, 2, 5, 4, 1 ]
vertex  6 -> Algebra 1502    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  7 -> Algebra 1262    permutation [ 7, 1, 2, 3, 4, 5, 6, 8 ]
vertex  8 -> Algebra 1495    permutation [ 2, 1, 4, 5, 6, 8, 7, 3 ]

Algebra 1502

Quiver

[ 1, 2 ], [ 1, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 7 ]

Relations

[ 5, 1, 3 ] 
[ 6, 8, 1, 3 ] 
[ 1, 3, 5 ] 
[ 6, 8, 7 ] 
[ 1, 3, 6, 8 ] 
[ 7, 6, 8 ] 
[ 3, 5, 1 ] - [ 3, 6, 8, 1 ] 
[ 8, 1, 3, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 1 1 0 0 1 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 0 1 1 0 1)
(1 1 0 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(1 1 0 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1451    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1501    permutation [ 1, 2, 6, 4, 5, 3, 7, 8 ]
vertex  4 -> Algebra 1368    permutation [ 1, 8, 7, 6, 2, 5, 4, 3 ]
vertex  6 -> Algebra 1137    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1455    permutation [ 2, 1, 5, 3, 6, 8, 7, 4 ]

Algebra 1508

Quiver

[ 1, 3 ], [ 1, 8 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 1 ], [ 5, 2 ], [ 6, 1 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 3, 5, 1 ] 
[ 8, 5, 1 ] 
[ 3, 5, 2 ] 
[ 2, 3, 5 ] 
[ 5, 1, 8 ] 
[ 5, 1, 3 ] - [ 5, 2, 3 ] 
[ 1, 3, 5 ] - [ 1, 8, 5 ] 

Cartan matrix

(1 0 1 0 1 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 0 1 0 0 0)
(1 1 1 1 1 0 0 0)
(1 1 1 0 1 0 0 0)
(1 0 1 0 1 1 0 1)
(1 0 1 0 1 1 1 1)
(0 1 0 0 1 0 0 1)

Good mutations

vertex  2 -> Algebra 1566    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1457    permutation [ 2, 3, 5, 8, 1, 7, 6, 4 ]
vertex  4 -> Algebra 1481    permutation [ 2, 3, 8, 4, 1, 7, 6, 5 ]
vertex  5 -> Algebra 1500    permutation [ 3, 5, 7, 6, 1, 2, 8, 4 ]
vertex  7 -> Algebra 1199    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1198    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1512

Quiver

[ 1, 3 ], [ 1, 8 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 5, 6 ], [ 6, 1 ], [ 6, 2 ], [ 7, 1 ], [ 8, 6 ]

Relations

[ 3, 6, 1 ] 
[ 8, 6, 1 ] 
[ 3, 6, 2 ] 
[ 2, 3, 6 ] 
[ 6, 1, 8 ] 
[ 6, 1, 3 ] - [ 6, 2, 3 ] 
[ 1, 3, 6 ] - [ 1, 8, 6 ] 

Cartan matrix

(1 0 1 0 0 1 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 0 0 1 0 0)
(1 1 1 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(1 1 1 0 0 1 0 0)
(1 0 1 0 0 1 1 1)
(0 1 0 0 0 1 0 1)

Good mutations

vertex  2 -> Algebra 1469    permutation [ 2, 6, 7, 8, 3, 5, 4, 1 ]
vertex  3 -> Algebra 1495    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  4 -> Algebra 1382    permutation [ 6, 2, 7, 8, 3, 5, 4, 1 ]
vertex  6 -> Algebra 1559    permutation [ 1, 2, 7, 8, 3, 5, 4, 6 ]
vertex  7 -> Algebra 1498    permutation [ 2, 3, 4, 5, 6, 1, 7, 8 ]
vertex  8 -> Algebra 1206    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1517

Quiver

[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 2 ], [ 4, 5 ], [ 7, 1 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 8, 4, 1 ] 
[ 3, 8, 4, 2 ] 
[ 8, 4, 2, 3 ] 
[ 1, 8, 4 ] 
[ 2, 3, 8, 4 ] 
[ 4, 1, 8 ] - [ 4, 2, 3, 8 ] 

Cartan matrix

(1 0 0 0 0 1 0 1)
(0 1 1 0 0 1 0 1)
(0 0 1 1 1 1 0 1)
(1 1 1 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 0 0 1 0 0)
(1 0 0 0 0 1 1 1)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1294    permutation [ 3, 4, 1, 2, 5, 8, 6, 7 ]
vertex  3 -> Algebra 1388    permutation [ 1, 2, 7, 3, 6, 4, 5, 8 ]
vertex  4 -> Algebra 1297    permutation [ 2, 8, 3, 6, 4, 7, 1, 5 ]
vertex  5 -> Algebra 1447    permutation [ 3, 5, 7, 1, 2, 8, 6, 4 ]
vertex  6 -> Algebra 1483    permutation [ 2, 3, 6, 5, 8, 1, 7, 4 ]
vertex  7 -> Algebra 1398    permutation [ 3, 4, 2, 7, 5, 8, 6, 1 ]
vertex  8 -> Algebra 1223    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1528

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 6, 2 ], [ 7, 6 ], [ 8, 6 ]

Relations

[ 4, 3, 1 ] 
[ 6, 2, 3, 1 ] 
[ 3, 1, 6, 2 ] 
[ 8, 6, 2 ] 
[ 3, 1, 4 ] 
[ 6, 2, 8 ] 
[ 1, 4, 3 ] - [ 1, 6, 2, 3 ] 
[ 2, 3, 1, 6 ] - [ 2, 8, 6 ] 

Cartan matrix

(1 1 1 1 1 1 0 0)
(1 1 1 0 1 1 0 1)
(1 0 1 0 1 1 0 0)
(0 0 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 1 0 1 1 0 0)
(0 1 1 0 1 1 1 0)
(0 0 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1308    permutation [ 2, 7, 1, 8, 6, 3, 5, 4 ]
vertex  2 -> Algebra 1530    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1568    permutation [ 7, 1, 4, 5, 3, 6, 8, 2 ]
vertex  6 -> Algebra 1305    permutation [ 2, 6, 7, 8, 1, 3, 5, 4 ]
vertex  7 -> Algebra 1292    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1530

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 1 ], [ 2, 3 ], [ 2, 5 ], [ 3, 6 ], [ 4, 2 ], [ 6, 2 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 4, 2, 1 ] 
[ 6, 2, 1 ] 
[ 3, 6, 2 ] 
[ 6, 2, 3 ] 
[ 2, 1, 4 ] 
[ 1, 4, 2 ] - [ 1, 6, 2 ] 
[ 2, 1, 6 ] - [ 2, 3, 6 ] 

Cartan matrix

(1 1 0 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(0 1 0 0 1 1 0 0)
(0 1 0 0 1 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1535    permutation [ 3, 7, 1, 8, 6, 2, 5, 4 ]
vertex  2 -> Algebra 1291    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1528    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1483    permutation [ 4, 1, 7, 5, 6, 3, 8, 2 ]
vertex  5 -> Algebra 1534    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1405    permutation [ 1, 4, 7, 5, 6, 3, 8, 2 ]
vertex  7 -> Algebra 1294    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1395    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1531

Quiver

[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 6 ], [ 4, 1 ], [ 6, 1 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 2, 3, 6, 1 ] 
[ 3, 6, 1, 2 ] 
[ 6, 1, 2, 3 ] 
[ 1, 2, 3, 6 ] 

Cartan matrix

(1 1 1 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(1 0 1 0 0 1 1 0)
(1 1 1 1 1 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1294    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1456    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1294    permutation [ 3, 6, 1, 8, 7, 2, 5, 4 ]
vertex  4 -> Algebra 1397    permutation [ 3, 6, 8, 4, 7, 2, 5, 1 ]
vertex  5 -> Algebra 1535    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  6 -> Algebra 1456    permutation [ 6, 3, 1, 8, 7, 2, 5, 4 ]
vertex  7 -> Algebra 1535    permutation [ 3, 7, 1, 8, 6, 2, 5, 4 ]
vertex  8 -> Algebra 1397    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1532

Quiver

[ 1, 5 ], [ 2, 3 ], [ 2, 4 ], [ 2, 8 ], [ 3, 1 ], [ 5, 2 ], [ 6, 7 ], [ 7, 5 ], [ 8, 5 ]

Relations

[ 5, 2, 3, 1 ] 
[ 3, 1, 5, 2 ] 
[ 8, 5, 2 ] 
[ 1, 5, 2, 3 ] 
[ 5, 2, 8 ] 
[ 2, 3, 1, 5 ] - [ 2, 8, 5 ] 

Cartan matrix

(1 1 0 1 1 0 0 0)
(1 1 1 1 1 0 0 1)
(1 0 1 0 1 0 0 0)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 0 0 0)
(0 1 1 1 1 1 1 0)
(0 1 1 1 1 0 1 0)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1498    permutation [ 1, 3, 6, 7, 5, 2, 4, 8 ]
vertex  2 -> Algebra 1485    permutation [ 1, 5, 3, 8, 2, 7, 6, 4 ]
vertex  3 -> Algebra 1297    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1469    permutation [ 1, 5, 4, 8, 3, 7, 6, 2 ]
vertex  5 -> Algebra 1388    permutation [ 7, 1, 6, 3, 4, 5, 8, 2 ]
vertex  6 -> Algebra 1470    permutation [ 1, 5, 4, 8, 3, 7, 6, 2 ]

Algebra 1534

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 5 ], [ 3, 6 ], [ 4, 5 ], [ 5, 1 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 4, 5, 1 ] 
[ 6, 5, 1 ] 
[ 6, 5, 3 ] 
[ 5, 1, 4 ] 
[ 3, 6, 5 ] 
[ 1, 4, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 3, 6 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(1 1 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 0 1 1 1 0 0 0)
(1 0 1 0 1 1 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1574    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1530    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1568    permutation [ 7, 1, 4, 2, 5, 6, 8, 3 ]
vertex  4 -> Algebra 1486    permutation [ 1, 6, 2, 8, 3, 4, 7, 5 ]
vertex  5 -> Algebra 1304    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1489    permutation [ 1, 4, 2, 8, 3, 5, 7, 6 ]
vertex  7 -> Algebra 1308    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1406    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1535

Quiver

[ 1, 5 ], [ 2, 5 ], [ 3, 6 ], [ 4, 1 ], [ 5, 3 ], [ 6, 1 ], [ 6, 7 ], [ 8, 3 ]

Relations

[ 5, 3, 6, 1 ] 
[ 6, 1, 5, 3 ] 
[ 3, 6, 1, 5 ] 
[ 1, 5, 3, 6 ] 

Cartan matrix

(1 0 1 0 1 0 0 0)
(0 1 1 0 1 1 1 0)
(1 0 1 0 0 1 1 0)
(1 0 1 1 1 0 0 0)
(0 0 1 0 1 1 1 0)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1308    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1531    permutation [ 1, 5, 3, 4, 2, 6, 7, 8 ]
vertex  3 -> Algebra 1530    permutation [ 3, 6, 1, 8, 7, 5, 2, 4 ]
vertex  4 -> Algebra 1407    permutation [ 5, 8, 2, 7, 3, 1, 4, 6 ]
vertex  5 -> Algebra 1406    permutation [ 5, 8, 2, 7, 3, 1, 4, 6 ]
vertex  6 -> Algebra 1569    permutation [ 3, 7, 4, 2, 5, 6, 8, 1 ]
vertex  7 -> Algebra 1574    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1407    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1547

Quiver

[ 1, 4 ], [ 1, 6 ], [ 2, 4 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 1 ], [ 5, 8 ], [ 6, 5 ], [ 7, 6 ], [ 8, 6 ]

Relations

[ 6, 5, 1 ] 
[ 1, 4, 3 ] 
[ 3, 1, 4 ] 
[ 5, 1, 4 ] 
[ 8, 6, 5 ] 
[ 6, 5, 8 ] 
[ 4, 3, 1 ] - [ 4, 5, 1 ] 
[ 1, 4, 5 ] - [ 1, 6, 5 ] 
[ 5, 1, 6 ] - [ 5, 8, 6 ] 

Cartan matrix

(1 0 0 1 1 1 0 0)
(1 1 1 1 1 1 0 1)
(1 0 1 0 0 1 0 0)
(1 0 1 1 1 1 0 1)
(1 0 0 0 1 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1566    permutation [ 1, 5, 8, 7, 6, 4, 2, 3 ]
vertex  2 -> Algebra 1416    permutation [ 3, 5, 8, 7, 6, 4, 2, 1 ]
vertex  5 -> Algebra 1348    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1477    permutation [ 1, 4, 2, 8, 3, 5, 7, 6 ]
vertex  7 -> Algebra 1352    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1548

Quiver

[ 1, 3 ], [ 1, 5 ], [ 2, 4 ], [ 3, 6 ], [ 4, 1 ], [ 5, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 6 ]

Relations

[ 3, 6, 1 ] 
[ 5, 8, 6, 1 ] 
[ 6, 1, 3 ] 
[ 8, 6, 1, 5 ] 
[ 6, 1, 5, 8 ] 
[ 1, 3, 6 ] - [ 1, 5, 8, 6 ] 

Cartan matrix

(1 0 1 0 1 1 1 1)
(1 1 1 1 1 1 1 1)
(0 0 1 0 0 1 1 0)
(1 0 1 1 1 1 1 1)
(0 0 0 0 1 1 1 1)
(1 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 0 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1352    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1428    permutation [ 1, 5, 8, 6, 7, 4, 2, 3 ]
vertex  5 -> Algebra 1402    permutation [ 5, 8, 3, 7, 1, 2, 4, 6 ]
vertex  6 -> Algebra 1497    permutation [ 5, 8, 2, 4, 1, 7, 3, 6 ]
vertex  7 -> Algebra 1566    permutation [ 1, 5, 8, 7, 6, 4, 2, 3 ]
vertex  8 -> Algebra 1481    permutation [ 8, 5, 3, 7, 1, 2, 4, 6 ]

Algebra 1559

Quiver

[ 1, 8 ], [ 2, 8 ], [ 3, 1 ], [ 4, 2 ], [ 6, 1 ], [ 6, 2 ], [ 7, 6 ], [ 8, 4 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 8, 6, 1 ] 
[ 2, 8, 4 ] 
[ 1, 8, 6 ] 
[ 2, 8, 6 ] 
[ 4, 2, 8 ] 
[ 8, 4, 2 ] - [ 8, 6, 2 ] 
[ 6, 1, 8 ] - [ 6, 2, 8 ] 

Cartan matrix

(1 0 0 1 1 0 0 1)
(0 1 0 0 1 0 0 1)
(1 0 1 1 1 0 0 1)
(0 1 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 0 0 1 1 0 1)
(1 1 0 0 1 1 1 1)
(0 1 0 1 1 1 0 1)

Good mutations

vertex  2 -> Algebra 1407    permutation [ 6, 3, 7, 5, 1, 2, 4, 8 ]
vertex  3 -> Algebra 1563    permutation [ 6, 1, 7, 5, 3, 2, 4, 8 ]
vertex  4 -> Algebra 1447    permutation [ 4, 7, 3, 1, 2, 8, 5, 6 ]
vertex  5 -> Algebra 1569    permutation [ 8, 4, 7, 3, 1, 2, 5, 6 ]
vertex  7 -> Algebra 1388    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1512    permutation [ 1, 2, 5, 7, 6, 8, 3, 4 ]

Algebra 1560

Quiver

[ 1, 3 ], [ 2, 8 ], [ 3, 6 ], [ 4, 2 ], [ 6, 1 ], [ 6, 2 ], [ 6, 7 ], [ 8, 3 ], [ 8, 4 ], [ 8, 5 ]

Relations

[ 3, 6, 1 ] 
[ 2, 8, 4 ] 
[ 1, 3, 6 ] 
[ 2, 8, 3, 6 ] 
[ 3, 6, 2, 8 ] 
[ 4, 2, 8 ] 
[ 8, 3, 6, 2 ] - [ 8, 4, 2 ] 
[ 6, 1, 3 ] - [ 6, 2, 8, 3 ] 

Cartan matrix

(1 0 1 0 0 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 1 0 0 1 1 0)
(0 1 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 1 0 1 1 1 1)
(0 0 0 0 0 0 1 0)
(0 1 1 1 1 1 1 1)

Good mutations

vertex  2 -> Algebra 1476    permutation [ 3, 6, 7, 5, 1, 2, 4, 8 ]
vertex  3 -> Algebra 1476    permutation [ 2, 8, 5, 7, 4, 3, 1, 6 ]
vertex  5 -> Algebra 1477    permutation [ 2, 8, 5, 7, 4, 3, 1, 6 ]
vertex  6 -> Algebra 1416    permutation [ 4, 3, 7, 1, 6, 8, 5, 2 ]
vertex  7 -> Algebra 1477    permutation [ 3, 6, 7, 5, 1, 2, 4, 8 ]
vertex  8 -> Algebra 1416    permutation [ 1, 2, 5, 4, 8, 6, 7, 3 ]

Algebra 1562

Quiver

[ 1, 2 ], [ 1, 3 ], [ 2, 5 ], [ 2, 8 ], [ 6, 1 ], [ 6, 7 ], [ 8, 4 ], [ 8, 6 ]

Relations

[ 2, 8, 6, 1 ] 
[ 8, 6, 1, 2 ] 
[ 1, 2, 8, 6 ] 
[ 6, 1, 2, 8 ] 

Cartan matrix

(1 1 1 1 1 0 0 1)
(0 1 0 1 1 1 1 1)
(0 0 1 0 0 0 0 0)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(1 1 1 0 1 1 1 0)
(0 0 0 0 0 0 1 0)
(1 0 1 1 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1476    permutation [ 1, 6, 7, 5, 3, 8, 4, 2 ]
vertex  2 -> Algebra 1476    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1397    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1397    permutation [ 8, 6, 4, 3, 7, 2, 5, 1 ]
vertex  5 -> Algebra 1397    permutation [ 2, 8, 5, 7, 4, 1, 3, 6 ]
vertex  6 -> Algebra 1476    permutation [ 6, 8, 4, 3, 7, 2, 5, 1 ]
vertex  7 -> Algebra 1397    permutation [ 6, 1, 7, 5, 3, 8, 4, 2 ]
vertex  8 -> Algebra 1476    permutation [ 8, 2, 5, 7, 4, 1, 3, 6 ]

Algebra 1563

Quiver

[ 1, 2 ], [ 1, 6 ], [ 2, 5 ], [ 2, 8 ], [ 3, 1 ], [ 6, 8 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ], [ 8, 7 ]

Relations

[ 2, 8, 1 ] 
[ 6, 8, 1 ] 
[ 8, 1, 2 ] 
[ 6, 8, 7 ] 
[ 7, 6, 8 ] 
[ 8, 1, 6 ] - [ 8, 7, 6 ] 
[ 1, 2, 8 ] - [ 1, 6, 8 ] 

Cartan matrix

(1 1 0 1 1 1 0 1)
(0 1 0 1 1 0 1 1)
(1 1 1 1 1 1 0 1)
(0 0 0 1 0 0 0 0)
(0 0 0 0 1 0 0 0)
(0 0 0 1 0 1 0 1)
(0 0 0 0 0 1 1 0)
(1 0 0 1 0 1 1 1)

Good mutations

vertex  2 -> Algebra 1477    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1476    permutation [ 6, 8, 4, 3, 7, 2, 5, 1 ]
vertex  4 -> Algebra 1456    permutation [ 6, 8, 1, 4, 7, 2, 5, 3 ]
vertex  5 -> Algebra 1559    permutation [ 2, 6, 5, 7, 4, 1, 3, 8 ]
vertex  6 -> Algebra 1397    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra 1408    permutation [ 7, 3, 6, 5, 1, 8, 4, 2 ]
vertex  8 -> Algebra 1498    permutation [ 6, 4, 3, 1, 8, 2, 5, 7 ]

Algebra 1566

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 1 ], [ 6, 1 ], [ 7, 6 ], [ 8, 5 ]

Relations

[ 2, 3, 5, 1 ] 
[ 8, 5, 1 ] 
[ 3, 5, 1, 2 ] 
[ 5, 1, 2, 3 ] 
[ 5, 1, 8 ] 
[ 1, 2, 3, 5 ] - [ 1, 8, 5 ] 

Cartan matrix

(1 1 1 0 1 0 0 1)
(0 1 1 0 1 0 0 0)
(1 0 1 0 1 0 0 0)
(1 1 0 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(1 1 1 0 1 1 0 1)
(1 1 1 0 1 1 1 1)
(0 0 0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra 1547    permutation [ 1, 7, 8, 6, 2, 5, 4, 3 ]
vertex  2 -> Algebra 1485    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1508    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1548    permutation [ 1, 7, 8, 6, 2, 5, 4, 3 ]
vertex  5 -> Algebra 1498    permutation [ 2, 3, 7, 6, 1, 5, 8, 4 ]
vertex  7 -> Algebra 1412    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 1568

Quiver

[ 1, 6 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 6, 8 ], [ 7, 6 ], [ 8, 5 ], [ 8, 7 ]

Relations

[ 3, 5, 2 ] 
[ 6, 8, 5, 2 ] 
[ 5, 2, 3 ] 
[ 6, 8, 7 ] 
[ 5, 2, 6, 8 ] 
[ 7, 6, 8 ] 
[ 2, 3, 5 ] - [ 2, 6, 8, 5 ] 
[ 8, 5, 2, 6 ] - [ 8, 7, 6 ] 

Cartan matrix

(1 0 0 0 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 0 1 0 1 0 0 0)
(0 1 0 1 1 1 0 0)
(0 1 0 0 1 1 0 0)
(0 0 0 0 1 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 0 0 1 1 1 1)

Good mutations

vertex  1 -> Algebra 1528    permutation [ 8, 2, 6, 7, 1, 5, 4, 3 ]
vertex  2 -> Algebra 1534    permutation [ 8, 1, 2, 7, 6, 5, 4, 3 ]
vertex  4 -> Algebra 1528    permutation [ 2, 8, 5, 3, 4, 6, 1, 7 ]
vertex  5 -> Algebra 1416    permutation [ 4, 8, 7, 1, 6, 5, 3, 2 ]
vertex  6 -> Algebra 1416    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1534    permutation [ 2, 4, 8, 3, 5, 6, 1, 7 ]

Algebra 1569

Quiver

[ 1, 2 ], [ 1, 8 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ], [ 5, 1 ], [ 6, 1 ], [ 7, 1 ], [ 8, 5 ], [ 8, 6 ]

Relations

[ 2, 6, 1 ] 
[ 6, 1, 2 ] 
[ 1, 8, 5 ] 
[ 5, 1, 8 ] 
[ 6, 1, 8 ] 
[ 8, 5, 1 ] - [ 8, 6, 1 ] 
[ 1, 2, 6 ] - [ 1, 8, 6 ] 

Cartan matrix

(1 1 0 0 0 1 0 1)
(0 1 0 0 0 1 0 0)
(1 0 1 0 1 1 0 1)
(1 1 0 1 1 0 0 0)
(1 1 0 0 1 0 0 0)
(1 0 0 0 0 1 0 0)
(1 1 0 0 0 1 1 1)
(1 0 0 0 1 1 0 1)

Good mutations

vertex  1 -> Algebra 1455    permutation [ 6, 1, 8, 7, 2, 5, 4, 3 ]
vertex  2 -> Algebra 1486    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra 1474    permutation [ 6, 1, 7, 3, 2, 5, 4, 8 ]
vertex  4 -> Algebra 1456    permutation [ 6, 1, 8, 7, 2, 5, 4, 3 ]
vertex  6 -> Algebra 1535    permutation [ 8, 4, 1, 3, 5, 6, 2, 7 ]
vertex  7 -> Algebra 1559    permutation [ 5, 6, 4, 2, 7, 8, 3, 1 ]

Algebra 1570

Quiver

[ 1, 2 ], [ 2, 5 ], [ 2, 6 ], [ 3, 1 ], [ 3, 7 ], [ 4, 2 ], [ 5, 1 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 1, 2 ] 
[ 6, 3, 1, 2 ] 
[ 1, 2, 6, 3 ] 
[ 7, 6, 3 ] 
[ 1, 2, 5 ] 
[ 6, 3, 7 ] 
[ 2, 5, 1 ] - [ 2, 6, 3, 1 ] 
[ 3, 1, 2, 6 ] - [ 3, 7, 6 ] 

Cartan matrix

(1 1 0 0 0 1 0 0)
(1 1 1 0 1 1 0 0)
(1 1 1 0 0 1 1 0)
(1 1 1 1 1 1 0 0)
(1 0 0 0 1 0 0 0)
(1 0 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 0 1 1 1)

Good mutations

vertex  1 -> Algebra 1456    permutation [ 6, 3, 2, 8, 7, 1, 5, 4 ]
vertex  4 -> Algebra 1477    permutation [ 6, 3, 8, 4, 7, 1, 5, 2 ]
vertex  6 -> Algebra 1456    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1477    permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]

Algebra 1574

Quiver

[ 1, 5 ], [ 2, 5 ], [ 3, 6 ], [ 4, 1 ], [ 5, 3 ], [ 6, 1 ], [ 7, 6 ], [ 8, 3 ]

Relations

[ 5, 3, 6, 1 ] 
[ 6, 1, 5, 3 ] 
[ 3, 6, 1, 5 ] 
[ 1, 5, 3, 6 ] 

Cartan matrix

(1 0 1 0 1 0 0 0)
(0 1 1 0 1 1 0 0)
(1 0 1 0 0 1 0 0)
(1 0 1 1 1 0 0 0)
(0 0 1 0 1 1 0 0)
(1 0 0 0 1 1 0 0)
(1 0 0 0 1 1 1 0)
(1 0 1 0 0 1 0 1)

Good mutations

vertex  1 -> Algebra 1534    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra 1535    permutation [ 3, 7, 1, 8, 6, 5, 2, 4 ]
vertex  3 -> Algebra 1534    permutation [ 3, 7, 1, 8, 6, 5, 2, 4 ]
vertex  4 -> Algebra 1535    permutation [ 5, 8, 6, 2, 3, 1, 4, 7 ]
vertex  5 -> Algebra 1534    permutation [ 5, 8, 6, 2, 3, 1, 4, 7 ]
vertex  6 -> Algebra 1534    permutation [ 6, 4, 5, 7, 1, 3, 8, 2 ]
vertex  7 -> Algebra 1535    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra 1535    permutation [ 6, 4, 5, 7, 1, 3, 8, 2 ]