Algebra 19
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
Cartan matrix
(1 0 1 0 1 1 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 1 1 1 1)
(0 1 1 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 0 0 0 0 0 1)
Good mutations
vertex 5 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 88 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 20
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
Cartan matrix
(1 0 1 1 0 1 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 0 1 1 1)
(0 0 0 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 0 1)
Good mutations
vertex 3 -> Algebra 80 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 89 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 90 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 91 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 21
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 0 1 1 1 0 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 1 0 1 1)
(0 0 0 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 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 81 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 93 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 95 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 26
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 0 1 1 1)
(0 1 1 1 0 1 1 1)
(0 1 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 101 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 111 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 112 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 27
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 1 0 1 1)
(0 1 1 1 1 0 1 1)
(0 1 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 102 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 114 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 53
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 1 1)
(1 1 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 177 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 187 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 188 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 54
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 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 1 1)
(1 1 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 178 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 190 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 80
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 0 1 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 101 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 20 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 263 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 264 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 81
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 1 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(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 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 102 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 21 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 266 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 85
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 1 1)
(0 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 1)
(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 4 -> Algebra 89 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 5 -> Algebra 19 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 278 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 280 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 87
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
Cartan matrix
(1 0 1 0 1 1 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 1 1 0 1)
(0 1 1 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 0 0 0 0 0 1)
Good mutations
vertex 5 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 284 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 19 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 285 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 88
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
Cartan matrix
(1 0 1 0 1 1 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 0 1 1 1 0)
(0 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 1 1 0 1 1 1 1)
Good mutations
vertex 5 -> Algebra 280 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 285 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 19 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 89
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 4 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 4, 3 ]
[ 3, 6, 4 ]
[ 4, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 1 1)
(0 1 1 1 1 0 0 1)
(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 0 1)
Good mutations
vertex 4 -> Algebra 20 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 85 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 288 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 289 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 290 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 90
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
Cartan matrix
(1 0 1 1 0 0 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 1 1)
(0 0 0 1 0 0 1 0)
(0 0 0 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 0 0 1)
Good mutations
vertex 3 -> Algebra 263 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 291 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 93 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 20 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 293 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 91
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
Cartan matrix
(1 0 1 1 0 1 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 0 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 1 1 0 0 0)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 264 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 289 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 294 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 20 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 295 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 92
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
Cartan matrix
(1 0 1 1 0 1 1 0)
(1 1 0 0 0 0 0 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 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 4 -> Algebra 290 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 293 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 295 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 20 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 93
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
Cartan matrix
(1 0 1 1 0 0 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 1 1)
(0 0 0 1 0 0 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 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 266 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 297 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 21 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 90 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 299 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 95
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 0 1 1 1 0 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 1 1 0 1 0)
(0 0 0 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 5 -> Algebra 299 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 21 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 101
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 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)
(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 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 80 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 319 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 320 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 102
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 1 1 0 1 1)
(1 1 1 0 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 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)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 81 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 322 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 111
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 0 0 1 1)
(0 1 1 1 0 0 1 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 1 0)
(0 0 1 1 1 1 0 0)
(0 0 1 1 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 187 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 319 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 114 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 112
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 0 1 0 1)
(0 1 1 1 0 1 0 1)
(0 1 1 0 0 0 0 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)
(0 0 0 0 1 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 188 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 320 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 351 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 114
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 1 1 1 0 0 1 1)
(0 1 1 1 0 0 1 1)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 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 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 190 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 322 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 27 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 111 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 177
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
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 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 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 479 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 480 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 481 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 482 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 178
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
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 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 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 477 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 483 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 485 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 187
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
[ 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 1 1)
(1 1 1 0 0 0 0 0)
(0 0 1 1 0 0 1 0)
(0 0 1 1 1 1 0 0)
(0 0 1 1 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 111 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 480 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 190 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 188
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 3, 2, 8 ]
[ 2, 4, 3 ] - [ 2, 8, 3 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 1 0 1 0 1)
(1 1 1 0 0 0 0 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)
(0 0 0 0 1 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 112 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 481 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 510 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 190
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
[ 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 1 1)
(1 1 1 0 0 0 0 0)
(0 0 1 1 0 0 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 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 114 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 483 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 54 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 187 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 263
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(0 0 1 1 0 0 1 0)
(0 0 1 1 1 1 0 0)
(0 0 1 1 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 319 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 90 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 266 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 80 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 264
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 0 1 0 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 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)
(0 0 0 0 1 1 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 320 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 91 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 661 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 80 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 266
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
[ 3, 1, 8 ]
[ 1, 4, 3 ] - [ 1, 8, 3 ]
Cartan matrix
(1 0 1 1 0 0 1 1)
(1 1 1 0 0 0 0 0)
(1 0 1 0 0 0 0 0)
(0 0 1 1 0 0 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 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 322 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 93 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 81 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 263 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 278
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 1)
(0 1 1 1 1 1 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 288 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 693 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 279
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 0 1)
(0 1 1 1 1 0 0 1)
(0 1 1 0 1 0 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 289 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 5 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 694 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 695 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 280
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 4, 5 ], [ 5, 3 ], [ 6, 5 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 1 0)
(0 1 1 1 1 0 0 0)
(0 1 1 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 4 -> Algebra 290 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 5 -> Algebra 88 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 693 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 695 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 85 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 282
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
Cartan matrix
(1 0 1 0 1 0 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 1 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 0 0 0 0 0 1)
Good mutations
vertex 5 -> Algebra 700 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 284 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 701 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 284
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
Cartan matrix
(1 0 1 0 1 0 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 1 0 0 1)
(0 1 1 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 0 0 0 0 0 1)
Good mutations
vertex 5 -> Algebra 482 permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 282 permutation [ 1, 2, 3, 4, 5, 7, 6, 8 ]
vertex 8 -> Algebra 479 permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
Algebra 285
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 6 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
Cartan matrix
(1 0 1 0 1 1 0 0)
(1 1 0 0 0 0 0 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)
(0 0 0 0 0 1 1 0)
(0 1 1 0 1 1 0 1)
Good mutations
vertex 5 -> Algebra 695 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 479 permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex 7 -> Algebra 88 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 87 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 288
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 6, 3 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 1)
(0 1 1 1 1 1 0 1)
(0 0 0 0 1 0 0 0)
(0 1 1 0 0 1 0 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 291 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 5 -> Algebra 278 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 89 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 712 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 289
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 4, 3 ]
[ 3, 6, 4 ]
[ 4, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 0 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 0 1)
(0 1 1 1 1 0 0 1)
(0 0 0 0 1 0 0 0)
(0 0 0 1 1 1 0 0)
(0 0 0 1 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 91 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 279 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 713 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 89 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 714 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 290
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ], [ 6, 4 ], [ 6, 7 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 4, 3 ]
[ 3, 6, 4 ]
[ 4, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 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 1 1 0 0 1 1 1)
Good mutations
vertex 4 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 280 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 712 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 714 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 89 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 291
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 3, 8 ], [ 4, 3 ], [ 4, 6 ], [ 5, 6 ], [ 7, 4 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 4, 3 ]
[ 3, 7, 4 ]
[ 4, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 1)
(0 1 1 1 0 1 0 1)
(0 0 0 0 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 90 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 297 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 288 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 8 -> Algebra 718 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 293
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
Cartan matrix
(1 0 1 1 0 0 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 1 0)
(0 0 0 1 0 0 1 0)
(0 0 0 1 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 0 1 1)
Good mutations
vertex 4 -> Algebra 718 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 299 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 90 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 294
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 5, 6 ], [ 6, 4 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
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 0 0)
(0 0 0 1 0 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 3 -> Algebra 661 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 485 permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 91 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 477 permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
Algebra 295
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
Cartan matrix
(1 0 1 1 0 1 0 0)
(1 1 0 0 0 0 0 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)
(0 0 0 0 1 1 1 0)
(0 1 1 1 0 1 0 1)
Good mutations
vertex 4 -> Algebra 714 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 477 permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex 7 -> Algebra 92 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 91 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 297
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 4 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 4, 3 ]
[ 3, 7, 4 ]
[ 4, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 1)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 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 1 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 93 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 291 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 727 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 299
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 4 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
Cartan matrix
(1 0 1 1 0 0 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 1 0 0 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)
(0 0 0 0 1 1 1 0)
(0 1 1 1 0 0 1 1)
Good mutations
vertex 4 -> Algebra 727 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 95 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 293 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 93 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 319
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 1 0 0 1 1)
(1 1 1 0 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 0 0 1 0)
(0 1 1 1 1 1 0 0)
(0 1 1 1 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 111 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 263 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 322 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 101 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 320
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 1 0 1 0 1)
(1 1 1 0 0 0 0 0)
(0 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)
(0 0 0 0 1 1 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 112 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 264 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 767 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 101 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 322
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
[ 2, 1, 8 ]
[ 1, 4, 2 ] - [ 1, 8, 2 ]
Cartan matrix
(1 1 1 1 0 0 1 1)
(1 1 1 0 0 0 0 0)
(0 0 1 0 0 0 0 0)
(0 1 1 1 0 0 1 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 114 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 266 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 102 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 319 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 351
Quiver
[ 1, 2 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
[ 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 0 0)
(0 0 1 1 0 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 510 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 767 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 112 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 477
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
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 0 1 0)
(0 0 0 1 1 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 1 0 0 0 1)
Good mutations
vertex 4 -> Algebra 178 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 295 permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 294 permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
Algebra 479
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 4 ], [ 3, 1 ], [ 4, 5 ], [ 5, 2 ], [ 6, 4 ], [ 6, 7 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 4, 5, 2 ]
[ 1, 2, 3 ]
[ 5, 2, 4 ]
[ 2, 4, 5 ]
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 1 0 0 0)
(0 1 1 0 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 4 -> Algebra 177 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 285 permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex 7 -> Algebra 701 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex 8 -> Algebra 284 permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
Algebra 480
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
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 1 0)
(0 1 1 1 1 1 0 0)
(0 1 1 1 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 187 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 695 permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex 5 -> Algebra 483 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 177 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 694 permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
Algebra 481
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
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 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)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 188 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 701 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex 6 -> Algebra 986 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 177 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 700 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
Algebra 482
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
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 0 1 1 1)
(0 1 1 1 1 0 0 1)
(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 4 -> Algebra 284 permutation [ 1, 3, 2, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 694 permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex 7 -> Algebra 700 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex 8 -> Algebra 177 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 483
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
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 1 0)
(0 1 1 1 1 1 0 0)
(0 0 0 0 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 190 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 714 permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex 5 -> Algebra 178 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 480 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 713 permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
Algebra 485
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 8 ], [ 3, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
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 0 1 1)
(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 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 294 permutation [ 1, 3, 2, 4, 6, 5, 7, 8 ]
vertex 5 -> Algebra 713 permutation [ 1, 3, 2, 5, 6, 4, 7, 8 ]
vertex 8 -> Algebra 178 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 510
Quiver
[ 2, 1 ], [ 2, 4 ], [ 2, 8 ], [ 3, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 2 ]
[ 8, 3, 2 ]
[ 3, 2, 4 ]
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
[ 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 0 0)
(0 0 1 1 0 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 351 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 986 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 188 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 661
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 3 ], [ 3, 1 ], [ 4, 3 ], [ 5, 6 ], [ 6, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 4, 3, 1 ]
[ 8, 3, 1 ]
[ 3, 1, 4 ]
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
[ 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 0 0)
(0 0 1 1 0 1 1 0)
(0 0 0 0 1 0 1 0)
(0 0 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 767 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 294 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 264 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 693
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 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 0 0 0 0 1 1 0)
(0 1 1 0 0 0 1 1)
Good mutations
vertex 4 -> Algebra 712 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 280 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 278 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 694
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ], [ 6, 7 ], [ 7, 5 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
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 0 1)
(0 1 1 0 1 1 0 1)
(0 1 1 0 0 1 1 1)
(0 0 0 0 1 0 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 713 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 5 -> Algebra 482 permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex 6 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 480 permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
Algebra 695
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 4, 5 ], [ 5, 3 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 5, 3 ]
[ 3, 6, 5 ]
[ 5, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 0 0)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 1 0 0)
(0 1 1 1 1 0 0 0)
(0 1 1 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 4 -> Algebra 714 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 5 -> Algebra 285 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 480 permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex 7 -> Algebra 280 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 279 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 698
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 5 ], [ 5, 6 ], [ 5, 7 ], [ 6, 4 ], [ 7, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 6, 4 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
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 0 1 1)
(0 1 1 0 1 1 1 1)
(0 0 0 1 0 1 0 0)
(0 1 1 0 0 0 1 1)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 5 -> Algebra 700 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 8 -> Algebra 986 permutation [ 1, 3, 2, 7, 4, 5, 6, 8 ]
Algebra 700
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 5, 7 ], [ 6, 7 ], [ 7, 4 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 7, 4 ]
[ 7, 4, 5 ]
[ 4, 5, 7 ]
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 0 0 1)
(0 1 1 0 1 0 1 1)
(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 5 -> Algebra 282 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 482 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex 7 -> Algebra 698 permutation [ 1, 2, 3, 4, 7, 6, 5, 8 ]
vertex 8 -> Algebra 481 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
Algebra 701
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
Cartan matrix
(1 0 1 0 1 0 0 0)
(1 1 0 0 0 0 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 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 0)
(0 1 1 0 1 0 0 1)
Good mutations
vertex 5 -> Algebra 481 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex 6 -> Algebra 479 permutation [ 1, 3, 2, 5, 4, 7, 6, 8 ]
vertex 8 -> Algebra 282 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 712
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 4, 5 ], [ 4, 6 ], [ 6, 3 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 6, 3 ]
[ 3, 7, 6 ]
[ 6, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 0)
(1 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 0 0 0)
(0 1 1 0 0 1 0 0)
(0 0 0 0 0 1 1 0)
(0 1 1 0 0 0 1 1)
Good mutations
vertex 4 -> Algebra 718 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 5 -> Algebra 693 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 290 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 288 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 713
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 8 ], [ 4, 5 ], [ 4, 6 ], [ 6, 3 ], [ 6, 7 ], [ 7, 4 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 7, 4 ]
[ 7, 4, 6 ]
[ 4, 6, 7 ]
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 0 1)
(0 0 0 0 1 0 0 0)
(0 1 1 0 0 1 1 1)
(0 0 0 1 1 0 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 4 -> Algebra 485 permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex 5 -> Algebra 694 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 289 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 483 permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
Algebra 714
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ], [ 6, 4 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 6, 4, 3 ]
[ 3, 6, 4 ]
[ 4, 3, 6 ]
Cartan matrix
(1 0 1 0 0 1 0 0)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 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)
(0 1 1 0 0 1 0 1)
Good mutations
vertex 4 -> Algebra 295 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 695 permutation [ 1, 2, 3, 5, 4, 6, 7, 8 ]
vertex 6 -> Algebra 483 permutation [ 1, 3, 2, 6, 4, 5, 7, 8 ]
vertex 7 -> Algebra 290 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 289 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 718
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 4, 3 ], [ 4, 6 ], [ 5, 6 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 4, 3 ]
[ 3, 7, 4 ]
[ 4, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 0)
(1 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 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 0 0 1 0 1 1 0)
(0 1 1 0 0 0 1 1)
Good mutations
vertex 4 -> Algebra 293 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 727 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 712 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 8 -> Algebra 291 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 727
Quiver
[ 1, 3 ], [ 2, 1 ], [ 3, 2 ], [ 3, 7 ], [ 4, 3 ], [ 4, 5 ], [ 5, 6 ], [ 7, 4 ], [ 8, 3 ]
Relations
[ 3, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, 3 ]
[ 7, 4, 3 ]
[ 3, 7, 4 ]
[ 4, 3, 7 ]
Cartan matrix
(1 0 1 0 0 0 1 0)
(1 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 0)
(0 0 0 1 1 1 1 0)
(0 1 1 0 0 0 1 1)
Good mutations
vertex 4 -> Algebra 299 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 718 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 8 -> Algebra 297 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 767
Quiver
[ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 3 ], [ 4, 2 ], [ 5, 6 ], [ 6, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]
Relations
[ 4, 2, 1 ]
[ 8, 2, 1 ]
[ 2, 1, 4 ]
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
[ 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 0 0)
(0 1 1 1 0 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 351 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 661 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 320 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 986
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 4, 2 ], [ 5, 6 ], [ 6, 4 ], [ 6, 7 ], [ 7, 5 ], [ 8, 2 ]
Relations
[ 2, 3, 1 ]
[ 3, 1, 2 ]
[ 1, 2, 3 ]
[ 6, 7, 5 ]
[ 7, 5, 6 ]
[ 5, 6, 7 ]
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 0 0)
(0 1 1 1 0 1 1 0)
(0 0 0 0 1 0 1 0)
(0 1 1 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 510 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 481 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 698 permutation [ 1, 3, 2, 5, 6, 7, 4, 8 ]