Algebra 466

Quiver

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

Relations

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

Cartan matrix

(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 0 0 0 0 1)
(0 0 1 1 0 1 1 0)
(0 0 1 1 1 0 0 0)
(0 0 0 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  622    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  900    permutation [ 1, 2, 8, 5, 6, 4, 7, 3 ]
vertex  7 -> Algebra  905    permutation [ 1, 2, 8, 5, 4, 7, 6, 3 ]

Algebra 472

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  628    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  925    permutation [ 1, 2, 8, 5, 6, 4, 7, 3 ]

Algebra 622

Quiver

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

Relations

[ 3, 8, 1 ] 
[ 3, 8, 4 ] 
[ 6, 5, 4 ] 
[ 4, 6, 5 ] 
[ 5, 4, 6 ] 
[ 1, 3, 8 ] 
[ 4, 3, 8 ] 
[ 8, 1, 3 ] - [ 8, 4, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  466    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra 1075    permutation [ 2, 1, 8, 5, 6, 4, 7, 3 ]
vertex  7 -> Algebra 1081    permutation [ 2, 1, 8, 5, 4, 7, 6, 3 ]

Algebra 628

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  472    permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1101    permutation [ 2, 1, 8, 5, 6, 4, 7, 3 ]

Algebra 645

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  751    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra  905    permutation [ 2, 3, 8, 6, 1, 7, 5, 4 ]

Algebra 751

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  645    permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex  5 -> Algebra 1081    permutation [ 3, 2, 8, 6, 1, 7, 5, 4 ]

Algebra 900

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1075    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  925    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  466    permutation [ 1, 2, 8, 6, 4, 5, 7, 3 ]

Algebra 905

Quiver

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

Relations

[ 8, 3, 2 ] 
[ 2, 8, 3 ] 
[ 5, 8, 3 ] 
[ 5, 7, 4 ] 
[ 7, 4, 5 ] 
[ 8, 3, 5 ] 
[ 4, 5, 7 ] 
[ 3, 2, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1081    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  466    permutation [ 1, 2, 8, 5, 4, 7, 6, 3 ]
vertex  7 -> Algebra  645    permutation [ 5, 1, 2, 8, 7, 4, 6, 3 ]

Algebra 925

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra 1101    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  472    permutation [ 1, 2, 8, 6, 4, 5, 7, 3 ]
vertex  5 -> Algebra  900    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]

Algebra 1075

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  900    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra 1101    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex  5 -> Algebra  622    permutation [ 2, 1, 8, 6, 4, 5, 7, 3 ]

Algebra 1081

Quiver

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

Relations

[ 8, 3, 2 ] 
[ 2, 8, 3 ] 
[ 5, 8, 3 ] 
[ 5, 7, 4 ] 
[ 7, 4, 5 ] 
[ 8, 3, 5 ] 
[ 4, 5, 7 ] 
[ 3, 2, 8 ] - [ 3, 5, 8 ] 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  905    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  6 -> Algebra  622    permutation [ 2, 1, 8, 5, 4, 7, 6, 3 ]
vertex  7 -> Algebra  751    permutation [ 5, 2, 1, 8, 7, 4, 6, 3 ]

Algebra 1101

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  925    permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex  4 -> Algebra  628    permutation [ 2, 1, 8, 6, 4, 5, 7, 3 ]
vertex  5 -> Algebra 1075    permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]