Algebra 274
Quiver
[ 1, 5 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 5, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 4, 2 ]
[ 2, 3, 4 ]
[ 8, 3, 4 ]
[ 3, 1, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 1, 5, 3 ] - [ 1, 8, 3 ]
[ 4, 2, 3 ] - [ 4, 8, 3 ]
[ 3, 1, 8 ] - [ 3, 4, 8 ]
Cartan matrix
(1 0 1 0 1 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 1)
(0 0 1 1 1 0 1 0)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 367 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 683 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 367
Quiver
[ 1, 5 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 2 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 5, 2, 1 ]
[ 8, 2, 1 ]
[ 3, 4, 8, 2 ]
[ 4, 8, 2, 3 ]
[ 8, 2, 3, 4 ]
[ 2, 1, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 1, 5, 2 ] - [ 1, 8, 2 ]
[ 2, 1, 8 ] - [ 2, 3, 4, 8 ]
Cartan matrix
(1 1 1 0 1 0 1 1)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 1)
(0 1 0 1 0 0 0 1)
(0 1 1 1 1 0 1 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 853 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 274 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 862 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 683
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]
Relations
[ 5, 3, 8, 1 ]
[ 3, 8, 4, 2 ]
[ 2, 3, 8, 4 ]
[ 3, 8, 1, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 1, 5, 3, 8 ]
[ 4, 2, 3, 8 ]
[ 8, 1, 5, 3 ] - [ 8, 4, 2, 3 ]
Cartan matrix
(1 0 1 0 1 0 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 1 0 0 0 1)
(0 1 1 1 0 0 0 0)
(0 0 1 1 1 0 1 1)
(0 0 1 1 1 1 0 1)
(0 0 0 0 0 1 1 0)
(1 1 1 1 1 0 1 1)
Good mutations
vertex 1 -> Algebra 1196 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 862 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 702 permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex 4 -> Algebra 903 permutation [ 2, 8, 1, 6, 5, 7, 4, 3 ]
vertex 8 -> Algebra 274 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 697
Quiver
[ 1, 7 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 3 ], [ 8, 3 ]
Relations
[ 7, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 5, 2 ]
[ 5, 6, 4 ]
[ 2, 3, 5 ]
[ 6, 4, 5 ]
[ 8, 3, 5 ]
[ 4, 5, 6 ]
[ 3, 1, 7 ]
[ 1, 7, 3 ] - [ 1, 8, 3 ]
[ 5, 2, 3 ] - [ 5, 8, 3 ]
[ 3, 1, 8 ] - [ 3, 5, 8 ]
Cartan matrix
(1 0 1 0 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 1 1 0 1)
(0 1 1 1 1 0 0 1)
(0 1 1 0 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 1 0 1 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 903 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 1196 permutation [ 2, 1, 8, 7, 5, 4, 6, 3 ]
vertex 8 -> Algebra 1213 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 702
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]
Relations
[ 5, 3, 1 ]
[ 1, 5, 3 ]
[ 4, 2, 3 ]
[ 2, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 2, 3, 8 ]
[ 5, 3, 8 ]
[ 3, 4, 2 ] - [ 3, 8, 2 ]
[ 8, 2, 3 ] - [ 8, 5, 3 ]
[ 3, 1, 5 ] - [ 3, 8, 5 ]
Cartan matrix
(1 0 0 0 1 0 1 0)
(1 1 1 0 0 0 0 0)
(1 1 1 1 1 0 1 1)
(0 1 0 1 0 0 0 0)
(0 0 1 1 1 0 1 0)
(0 0 1 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 1215 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 733 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 8 -> Algebra 683 permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
Algebra 733
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]
Relations
[ 5, 4, 1 ]
[ 3, 4, 8, 2 ]
[ 4, 8, 2, 3 ]
[ 1, 5, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 2, 3, 4, 8 ]
[ 5, 4, 8 ]
[ 8, 2, 3, 4 ] - [ 8, 5, 4 ]
[ 4, 1, 5 ] - [ 4, 8, 5 ]
Cartan matrix
(1 0 0 0 1 0 1 0)
(1 1 1 1 0 0 0 0)
(1 0 1 1 1 0 1 1)
(1 1 0 1 1 0 1 1)
(0 0 0 1 1 0 1 0)
(0 0 0 1 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 1213 permutation [ 2, 1, 4, 6, 5, 7, 3, 8 ]
vertex 3 -> Algebra 702 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 8 -> Algebra 903 permutation [ 2, 4, 1, 6, 5, 7, 3, 8 ]
Algebra 853
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ]
Relations
[ 2, 3, 4, 8, 1 ]
[ 3, 4, 8, 1, 2 ]
[ 4, 8, 1, 2, 3 ]
[ 8, 1, 2, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 1, 2, 3, 4, 8 ]
Cartan matrix
(1 1 1 1 0 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 0 0 0 1)
(1 1 0 1 0 0 0 1)
(1 1 1 1 1 0 1 0)
(1 1 1 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 367 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 1355 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 862
Quiver
[ 1, 5 ], [ 2, 3 ], [ 2, 8 ], [ 3, 4 ], [ 4, 2 ], [ 5, 2 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ], [ 8, 4 ]
Relations
[ 5, 2, 8, 1 ]
[ 3, 4, 2 ]
[ 4, 2, 3 ]
[ 2, 8, 1, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 1, 5, 2, 8 ]
[ 4, 2, 8 ]
[ 8, 1, 5, 2 ] - [ 8, 4, 2 ]
[ 2, 3, 4 ] - [ 2, 8, 4 ]
Cartan matrix
(1 1 1 0 1 0 1 0)
(1 1 1 1 0 0 0 1)
(0 0 1 1 0 0 0 0)
(0 1 0 1 0 0 0 0)
(0 1 1 1 1 0 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 0 1 1)
Good mutations
vertex 3 -> Algebra 683 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 1275 permutation [ 1, 2, 8, 3, 5, 6, 7, 4 ]
vertex 8 -> Algebra 367 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 903
Quiver
[ 1, 7 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 2 ], [ 8, 2 ]
Relations
[ 7, 2, 1 ]
[ 8, 2, 1 ]
[ 3, 5, 8, 2 ]
[ 5, 8, 2, 3 ]
[ 5, 6, 4 ]
[ 6, 4, 5 ]
[ 8, 2, 3, 5 ]
[ 4, 5, 6 ]
[ 2, 1, 7 ]
[ 1, 7, 2 ] - [ 1, 8, 2 ]
[ 2, 1, 8 ] - [ 2, 3, 5, 8 ]
Cartan matrix
(1 1 1 0 0 0 1 1)
(1 1 1 0 1 1 0 1)
(0 0 1 0 1 1 0 1)
(0 1 0 1 1 0 0 1)
(0 1 0 0 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 1 1 0 1 1 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 1421 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 697 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 683 permutation [ 3, 1, 8, 7, 5, 4, 6, 2 ]
vertex 8 -> Algebra 733 permutation [ 3, 1, 7, 2, 5, 4, 6, 8 ]
Algebra 935
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ]
Relations
[ 2, 3, 8, 4, 1 ]
[ 3, 8, 4, 1, 2 ]
[ 8, 4, 1, 2, 3 ]
[ 1, 2, 3, 8, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 4, 1, 2, 3, 8 ]
Cartan matrix
(1 1 1 0 0 0 0 1)
(0 1 1 1 0 1 1 1)
(1 0 1 1 0 1 1 1)
(1 1 1 1 0 1 1 0)
(1 1 1 1 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 6 -> Algebra 1433 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 1355 permutation [ 4, 1, 2, 3, 6, 5, 7, 8 ]
Algebra 943
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 2, 3, 8, 4, 1 ]
[ 3, 8, 4, 1, 2 ]
[ 8, 4, 1, 2, 3 ]
[ 1, 2, 3, 8, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 1, 2, 3, 8 ]
Cartan matrix
(1 1 1 0 0 0 0 1)
(0 1 1 1 1 0 1 1)
(1 0 1 1 1 0 1 1)
(1 1 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 0 1 1 0 1 1)
Good mutations
vertex 4 -> Algebra 1437 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 1436 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1196
Quiver
[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ], [ 8, 5 ]
Relations
[ 8, 5, 1 ]
[ 3, 8, 4, 2 ]
[ 2, 3, 8, 4 ]
[ 1, 8, 5 ]
[ 3, 8, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 2, 3, 8 ]
[ 8, 4, 2, 3 ] - [ 8, 5, 3 ]
[ 5, 1, 8 ] - [ 5, 3, 8 ]
Cartan matrix
(1 1 0 1 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)
(1 0 1 1 1 0 1 1)
(1 0 1 1 1 1 0 1)
(0 0 0 0 0 1 1 0)
(0 1 1 1 1 0 1 1)
Good mutations
vertex 1 -> Algebra 683 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 1215 permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex 4 -> Algebra 697 permutation [ 2, 1, 8, 6, 5, 7, 4, 3 ]
Algebra 1213
Quiver
[ 1, 7 ], [ 2, 3 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 3 ], [ 8, 1 ], [ 8, 5 ]
Relations
[ 7, 3, 8, 1 ]
[ 3, 8, 5, 2 ]
[ 5, 6, 4 ]
[ 2, 3, 8, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 3, 8, 1, 7 ]
[ 1, 7, 3, 8 ]
[ 5, 2, 3, 8 ]
[ 8, 1, 7, 3 ] - [ 8, 5, 2, 3 ]
Cartan matrix
(1 0 1 0 0 0 1 0)
(1 1 1 0 0 0 0 1)
(1 0 1 0 1 1 0 1)
(0 1 1 1 1 0 0 0)
(0 1 1 0 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 0 1 0 1 1 1 1)
(1 1 1 0 1 1 1 1)
Good mutations
vertex 1 -> Algebra 1438 permutation [ 2, 7, 1, 3, 5, 4, 6, 8 ]
vertex 2 -> Algebra 733 permutation [ 2, 1, 7, 3, 5, 4, 6, 8 ]
vertex 3 -> Algebra 1214 permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
vertex 7 -> Algebra 1215 permutation [ 2, 1, 3, 7, 5, 4, 6, 8 ]
vertex 8 -> Algebra 697 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1214
Quiver
[ 1, 7 ], [ 2, 3 ], [ 3, 1 ], [ 3, 5 ], [ 3, 8 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 6, 4 ], [ 7, 3 ], [ 8, 2 ], [ 8, 7 ]
Relations
[ 7, 3, 1 ]
[ 1, 7, 3 ]
[ 5, 2, 3 ]
[ 5, 6, 4 ]
[ 2, 3, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 2, 3, 8 ]
[ 7, 3, 8 ]
[ 3, 5, 2 ] - [ 3, 8, 2 ]
[ 8, 2, 3 ] - [ 8, 7, 3 ]
[ 3, 1, 7 ] - [ 3, 8, 7 ]
Cartan matrix
(1 0 0 0 0 0 1 0)
(1 1 1 0 0 0 0 0)
(1 1 1 0 1 1 1 1)
(0 1 0 1 1 0 0 0)
(0 1 0 0 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 0 1 0 1 1 1 0)
(0 1 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 1437 permutation [ 8, 7, 1, 2, 5, 4, 6, 3 ]
vertex 8 -> Algebra 1213 permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
Algebra 1215
Quiver
[ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 4, 2 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]
Relations
[ 3, 8, 5, 1 ]
[ 4, 2, 3 ]
[ 2, 3, 4 ]
[ 1, 3, 8, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 2, 3, 8 ]
[ 5, 1, 3, 8 ]
[ 3, 4, 2 ] - [ 3, 8, 2 ]
[ 8, 2, 3 ] - [ 8, 5, 1, 3 ]
Cartan matrix
(1 1 1 1 0 0 0 1)
(0 1 1 0 0 0 0 0)
(0 1 1 1 1 0 1 1)
(0 1 0 1 0 0 0 0)
(1 0 1 1 1 0 1 0)
(1 0 1 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 1 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 702 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 1422 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 1213 permutation [ 2, 1, 3, 6, 5, 7, 4, 8 ]
vertex 8 -> Algebra 1196 permutation [ 1, 2, 8, 4, 5, 6, 7, 3 ]
Algebra 1275
Quiver
[ 1, 5 ], [ 2, 8 ], [ 3, 1 ], [ 5, 2 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ], [ 8, 4 ]
Relations
[ 5, 2, 8, 3, 1 ]
[ 8, 3, 1, 5, 2 ]
[ 1, 5, 2, 8, 3 ]
[ 2, 8, 3, 1, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 1, 5, 2, 8 ]
Cartan matrix
(1 1 0 1 1 0 1 1)
(1 1 1 1 0 0 0 1)
(1 1 1 0 1 0 1 0)
(0 0 0 1 0 0 0 0)
(0 1 1 1 1 0 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 0 1 1 0)
(1 0 1 1 1 0 1 1)
Good mutations
vertex 4 -> Algebra 1421 permutation [ 8, 3, 1, 6, 5, 7, 4, 2 ]
vertex 8 -> Algebra 862 permutation [ 1, 2, 4, 8, 5, 6, 7, 3 ]
Algebra 1355
Quiver
[ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 8 ], [ 5, 6 ], [ 6, 1 ], [ 7, 5 ], [ 8, 1 ]
Relations
[ 2, 3, 4, 8, 1 ]
[ 5, 6, 1 ]
[ 3, 4, 8, 1, 2 ]
[ 4, 8, 1, 2, 3 ]
[ 8, 1, 2, 3, 4 ]
[ 6, 1, 5 ]
[ 1, 5, 6 ]
[ 1, 2, 3, 4, 8 ]
Cartan matrix
(1 1 1 1 1 0 0 0)
(0 1 1 1 0 0 0 1)
(1 0 1 1 1 0 0 1)
(1 1 0 1 1 0 0 1)
(0 0 0 0 1 1 0 0)
(1 1 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 1 0 1 0 0 1)
Good mutations
vertex 5 -> Algebra 853 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 935 permutation [ 2, 3, 4, 1, 6, 5, 7, 8 ]
Algebra 1421
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 5 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 1 ], [ 8, 1 ]
Relations
[ 2, 3, 5, 8, 1 ]
[ 3, 5, 8, 1, 2 ]
[ 5, 8, 1, 2, 3 ]
[ 5, 6, 4 ]
[ 6, 4, 5 ]
[ 8, 1, 2, 3, 5 ]
[ 4, 5, 6 ]
[ 1, 2, 3, 5, 8 ]
Cartan matrix
(1 1 1 0 1 1 0 0)
(0 1 1 0 1 1 0 1)
(1 0 1 0 1 1 0 1)
(1 1 0 1 1 0 0 1)
(1 1 0 0 1 1 0 1)
(0 0 0 1 0 1 0 0)
(1 1 1 0 1 1 1 0)
(1 1 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 903 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 1275 permutation [ 3, 8, 2, 7, 5, 4, 6, 1 ]
Algebra 1422
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 8 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 5 ]
Relations
[ 2, 3, 8, 5, 1 ]
[ 3, 8, 5, 1, 2 ]
[ 8, 5, 1, 2, 3 ]
[ 1, 2, 3, 8, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 1, 2, 3, 8 ]
Cartan matrix
(1 1 1 1 0 0 0 1)
(0 1 1 1 1 0 1 1)
(1 0 1 1 1 0 1 1)
(0 0 0 1 0 0 0 0)
(1 1 1 1 1 0 1 0)
(1 1 1 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 1 0 1 1)
Good mutations
vertex 3 -> Algebra 1215 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 1440 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
Algebra 1433
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 2, 3, 8, 4, 1 ]
[ 3, 8, 4, 1, 2 ]
[ 8, 4, 1, 2, 3 ]
[ 1, 2, 3, 8, 4 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
[ 4, 1, 2, 3, 8 ]
Cartan matrix
(1 1 1 0 0 0 0 1)
(0 1 1 1 0 0 1 1)
(1 0 1 1 0 0 1 1)
(1 1 1 1 0 0 1 0)
(1 1 1 1 1 1 0 0)
(1 1 1 1 0 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 0 0 1 1)
Good mutations
vertex 5 -> Algebra 1436 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 935 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1436
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 4 ]
Relations
[ 2, 3, 8, 4, 1 ]
[ 3, 8, 4, 1, 2 ]
[ 8, 4, 1, 2, 3 ]
[ 1, 2, 3, 8, 4 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
[ 4, 1, 2, 3, 8 ]
Cartan matrix
(1 1 1 0 0 0 0 1)
(0 1 1 1 0 0 1 1)
(1 0 1 1 0 0 1 1)
(1 1 1 1 0 0 1 0)
(1 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 1 1 1 0)
(1 1 0 1 0 0 1 1)
Good mutations
vertex 5 -> Algebra 943 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 1433 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 1437
Quiver
[ 1, 2 ], [ 1, 4 ], [ 2, 3 ], [ 3, 8 ], [ 4, 8 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 1 ], [ 8, 5 ]
Relations
[ 2, 3, 8, 1 ]
[ 4, 8, 1 ]
[ 3, 8, 1, 2 ]
[ 8, 1, 2, 3 ]
[ 4, 8, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 4, 8 ]
[ 8, 1, 4 ] - [ 8, 5, 4 ]
[ 1, 2, 3, 8 ] - [ 1, 4, 8 ]
Cartan matrix
(1 1 1 1 0 0 0 1)
(0 1 1 0 1 0 1 1)
(1 0 1 1 1 0 1 1)
(0 0 0 1 0 0 0 1)
(0 0 0 1 1 0 1 0)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 1 1 0 1 1)
Good mutations
vertex 1 -> Algebra 1438 permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
vertex 3 -> Algebra 1214 permutation [ 3, 4, 8, 6, 5, 7, 2, 1 ]
vertex 4 -> Algebra 943 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1438
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 4 ], [ 3, 8 ], [ 4, 8 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ], [ 8, 5 ]
Relations
[ 4, 8, 5, 1 ]
[ 3, 8, 2 ]
[ 4, 8, 2 ]
[ 8, 2, 3 ]
[ 1, 4, 8, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 1, 4, 8 ]
[ 8, 2, 4 ] - [ 8, 5, 1, 4 ]
[ 2, 3, 8 ] - [ 2, 4, 8 ]
Cartan matrix
(1 0 0 1 0 0 0 1)
(0 1 1 1 1 0 1 1)
(1 0 1 0 1 0 1 1)
(0 0 0 1 1 0 1 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 0 1 1 0 1 1)
Good mutations
vertex 2 -> Algebra 1440 permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]
vertex 3 -> Algebra 1213 permutation [ 3, 1, 4, 6, 5, 7, 2, 8 ]
vertex 4 -> Algebra 1437 permutation [ 4, 2, 3, 1, 5, 6, 7, 8 ]
Algebra 1440
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 8 ], [ 5, 1 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 5 ]
Relations
[ 2, 4, 8, 5, 1 ]
[ 4, 8, 5, 1, 2 ]
[ 8, 5, 1, 2, 4 ]
[ 1, 2, 4, 8, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 1, 2, 4, 8 ]
Cartan matrix
(1 1 0 1 0 0 0 1)
(0 1 0 1 1 0 1 1)
(1 0 1 1 1 0 1 1)
(1 0 0 1 1 0 1 1)
(1 1 0 1 1 0 1 0)
(1 1 0 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(1 1 0 0 1 0 1 1)
Good mutations
vertex 3 -> Algebra 1422 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 4 -> Algebra 1438 permutation [ 1, 4, 3, 2, 5, 6, 7, 8 ]