Algebra 3

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   18    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   22    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   23    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 4

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra   24    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   28    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 11

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra   51    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   55    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 18

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   24    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   82    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 22

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   82    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   96    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   97    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 23

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  7 -> Algebra   97    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 24

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   18    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  103    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 28

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   55    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  103    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  117    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 51

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  176    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  179    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  180    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 55

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   28    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  179    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  193    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 82

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  103    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   22    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  269    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   18    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 94

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  267    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  300    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   96    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  301    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 96

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  269    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  303    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   22    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   94    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  304    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 97

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  6 -> Algebra  304    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   23    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   22    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 103

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   28    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   82    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  325    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   24    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 115

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  191    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  323    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  357    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  117    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 117

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  193    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  325    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  360    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   28    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  115    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 176

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   51    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  304    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  478    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  303    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]

Algebra 179

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   55    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  478    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  486    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra   51    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  487    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 180

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  303    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  487    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra   51    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 191

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  115    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  484    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  516    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  193    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 193

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  117    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  486    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  519    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   55    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  191    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 267

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  323    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   94    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  667    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  269    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 269

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  325    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra   96    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  670    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   82    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  267    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 292

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  659    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  719    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  298    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  720    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 298

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  665    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  728    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  300    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra  292    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  729    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 300

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  667    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  487    permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex  5 -> Algebra   94    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  303    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  7 -> Algebra  298    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  8 -> Algebra  478    permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]

Algebra 301

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 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 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  5 -> Algebra  478    permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex  6 -> Algebra  304    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra   94    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 303

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  670    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  180    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra   96    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  300    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  176    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]

Algebra 304

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

(1 0 1 1 1 0 0 0)
(1 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 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  5 -> Algebra  176    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra   97    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  301    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra   96    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 323

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  115    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  267    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  773    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  325    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 325

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  117    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  269    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  776    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  103    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  323    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 349

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  508    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  765    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  355    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 355

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  514    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  771    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  357    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra  349    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 357

Quiver

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

Relations

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

Cartan matrix

(1 1 1 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 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  516    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  773    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  115    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  360    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  7 -> Algebra  355    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]

Algebra 360

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  519    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  776    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  117    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  357    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 478

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  179    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  301    permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex  6 -> Algebra  729    permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex  7 -> Algebra  176    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  300    permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]

Algebra 484

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  191    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  720    permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex  5 -> Algebra  988    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  486    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  719    permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]

Algebra 486

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  193    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  729    permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex  5 -> Algebra  989    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  179    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  484    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  728    permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]

Algebra 487

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  300    permutation [ 1, 3, 2, 4, 5, 7, 6, 8 ]
vertex  6 -> Algebra  728    permutation [ 1, 3, 2, 4, 6, 7, 5, 8 ]
vertex  7 -> Algebra  180    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  8 -> Algebra  179    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 508

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  349    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  985    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  514    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 514

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  355    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  987    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  516    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra  508    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 516

Quiver

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

Relations

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

Cartan matrix

(1 0 0 0 0 0 0 0)
(1 1 1 1 0 0 0 1)
(1 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 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  357    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  988    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  191    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  519    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  7 -> Algebra  514    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]

Algebra 519

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  360    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  2 -> Algebra  989    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  193    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  516    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 659

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  765    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  292    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  665    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 665

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  771    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  298    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  667    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra  659    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 667

Quiver

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

Relations

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

Cartan matrix

(1 0 1 1 0 0 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(0 0 1 1 0 0 0 0)
(0 0 1 1 1 0 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  2 -> Algebra  773    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  300    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  267    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  670    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  7 -> Algebra  665    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]

Algebra 670

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  776    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  303    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  269    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  667    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 692

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  711    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  8 -> Algebra  985    permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]

Algebra 711

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  717    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  5 -> Algebra  692    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  8 -> Algebra  987    permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]

Algebra 717

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  719    permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex  5 -> Algebra  726    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  6 -> Algebra  711    permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex  8 -> Algebra  988    permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]

Algebra 719

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  292    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  728    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  717    permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex  8 -> Algebra  484    permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]

Algebra 720

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  484    permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex  5 -> Algebra  729    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  292    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 726

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  728    permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex  6 -> Algebra  717    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  989    permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]

Algebra 728

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  298    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  487    permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex  6 -> Algebra  719    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  7 -> Algebra  726    permutation [ 1, 2, 3, 7, 5, 6, 4, 8 ]
vertex  8 -> Algebra  486    permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]

Algebra 729

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  486    permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex  5 -> Algebra  478    permutation [ 1, 3, 2, 4, 7, 5, 6, 8 ]
vertex  6 -> Algebra  720    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  298    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]

Algebra 765

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  349    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  659    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  771    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 771

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  355    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  665    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  773    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra  765    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]

Algebra 773

Quiver

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

Relations

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

Cartan matrix

(1 1 1 1 0 0 0 1)
(1 1 1 0 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 0 0 0 0)
(0 1 1 1 1 0 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  357    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  667    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  323    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  776    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  7 -> Algebra  771    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]

Algebra 776

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  360    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  3 -> Algebra  670    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  325    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  773    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]

Algebra 985

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  508    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  987    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  692    permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]

Algebra 987

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  514    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  988    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  6 -> Algebra  985    permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex  8 -> Algebra  711    permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]

Algebra 988

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(0 1 1 1 0 0 0 0)
(0 1 1 1 1 0 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  516    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  484    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  989    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  7 -> Algebra  987    permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex  8 -> Algebra  717    permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]

Algebra 989

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  519    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  486    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  7 -> Algebra  988    permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex  8 -> Algebra  726    permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]