Algebra 32
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 1 0 1 0 1 1)
(0 1 1 0 1 0 1 1)
(0 0 1 0 1 0 1 1)
(0 0 1 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)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 59
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 1 1)
(0 0 1 0 1 0 1 1)
(0 0 1 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)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 163 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 205 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 207 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 129
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 1 0 0 0 1 1)
(0 1 1 0 0 0 1 1)
(0 0 1 0 0 0 1 1)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 205 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 392 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 131
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 1 0 1 0 1 0)
(0 1 1 0 1 0 1 0)
(0 0 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 1 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 207 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 395 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 392 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 144
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 1 0 1 0 1 1 0)
(0 1 0 1 0 1 1 0)
(0 1 1 1 0 1 1 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 0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 220 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 421 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 416 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 419 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 150
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 1 0 1 1 0 1 0)
(0 1 0 1 1 0 1 0)
(0 1 1 1 1 0 1 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 0 0 1 1 0 1 1)
Good mutations
vertex 1 -> Algebra 226 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 431 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 426 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 163
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(0 1 1 0 1 0 1 1)
(0 1 1 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)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 239 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 444 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 451 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 453 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 205
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 1 1)
(0 0 1 0 0 0 1 1)
(0 0 1 1 1 0 0 1)
(0 0 1 0 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 451 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 549 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 207
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 0 1 0 1 0)
(0 0 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 1 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 453 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 552 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 549 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 220
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 1 0 1 1 0)
(1 1 1 1 0 1 1 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 0 0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 578 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 573 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 576 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 226
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 1 1 0 1 0)
(1 1 1 1 1 0 1 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 0 0 1 1 0 1 1)
Good mutations
vertex 1 -> Algebra 150 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 588 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 583 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 239
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 5 ], [ 3, 8 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 0 1 0 1 1)
(1 1 1 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)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 163 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 600 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 607 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 609 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 392
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 7 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 1 0 0 0 1 0)
(0 1 1 0 0 0 1 0)
(0 0 1 0 0 0 1 0)
(0 0 1 1 1 0 0 0)
(0 0 1 0 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 549 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 669 permutation [ 8, 1, 2, 3, 5, 4, 6, 7 ]
vertex 5 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 129 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 395
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 5 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 8, 5, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 3, 8 ]
[ 3, 2, 5 ] - [ 3, 8, 5 ]
Cartan matrix
(1 1 0 0 1 0 1 0)
(0 1 0 0 1 0 1 0)
(0 1 1 1 1 0 1 1)
(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 1 0 1 1)
Good mutations
vertex 1 -> Algebra 552 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 131 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 431 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 5 -> Algebra 908 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 416
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 1 0 1 0 0 1 0)
(0 1 0 1 0 0 1 0)
(0 1 1 1 0 0 1 1)
(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 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 573 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 932 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 426 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 419
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 1 0 1 0 1 0 0)
(0 1 0 1 0 1 0 0)
(0 1 1 1 0 1 0 1)
(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 0 1 0 1 0 1)
Good mutations
vertex 1 -> Algebra 576 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 934 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 444 permutation [ 1, 2, 4, 3, 6, 5, 7, 8 ]
vertex 7 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 421
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 6 ]
Relations
[ 6, 4, 2 ]
[ 4, 5, 3 ]
[ 2, 6, 4 ]
[ 5, 3, 4 ]
[ 8, 6, 4 ]
[ 3, 4, 5 ]
[ 6, 4, 8 ]
[ 4, 2, 6 ] - [ 4, 8, 6 ]
Cartan matrix
(1 1 0 0 0 1 1 0)
(0 1 0 0 0 1 1 0)
(0 1 1 1 0 1 1 1)
(0 1 0 1 1 1 1 1)
(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 1 1 1)
Good mutations
vertex 1 -> Algebra 578 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 144 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 937 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 934 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 426
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 1 0 1 0 0 1 0)
(0 1 0 1 0 0 1 0)
(0 1 1 1 0 0 1 1)
(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 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 583 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 663 permutation [ 8, 1, 2, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 150 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 416 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 431
Quiver
[ 1, 2 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 5 ]
Relations
[ 5, 4, 2 ]
[ 2, 5, 4 ]
[ 8, 5, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 4, 8 ]
[ 4, 2, 5 ] - [ 4, 8, 5 ]
Cartan matrix
(1 1 0 0 1 0 1 0)
(0 1 0 0 1 0 1 0)
(0 1 1 1 1 0 1 1)
(0 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 0 0 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 588 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 395 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 4 -> Algebra 150 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 946 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 444
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 4, 2 ]
[ 2, 3, 4 ]
[ 8, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 4, 8 ]
[ 4, 2, 3 ] - [ 4, 8, 3 ]
Cartan matrix
(1 1 1 0 0 0 0 0)
(0 1 1 0 0 0 0 0)
(0 0 1 1 0 0 0 0)
(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 1 -> Algebra 600 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 163 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 419 permutation [ 1, 2, 4, 3, 6, 5, 7, 8 ]
Algebra 451
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(0 1 1 0 0 0 1 1)
(0 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 0 0 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 607 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 205 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 934 permutation [ 1, 2, 4, 5, 6, 3, 7, 8 ]
vertex 5 -> Algebra 163 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 966 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 453
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(0 1 1 0 1 0 1 0)
(0 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 1 1 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 609 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 207 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 966 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 163 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 549
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 7 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 1 0 0 0 1 0)
(0 0 1 0 0 0 1 0)
(0 0 1 1 1 0 0 0)
(0 0 1 0 1 1 0 0)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 392 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 966 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 775 permutation [ 8, 2, 1, 3, 5, 4, 6, 7 ]
vertex 5 -> Algebra 207 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 205 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 552
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 3, 8 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 5 ]
Relations
[ 5, 3, 2 ]
[ 2, 5, 3 ]
[ 8, 5, 3 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 3, 8 ]
[ 3, 2, 5 ] - [ 3, 8, 5 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 1 0 1 0)
(1 1 1 1 1 0 1 1)
(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 1 0 1 1)
Good mutations
vertex 1 -> Algebra 395 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 207 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 588 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 5 -> Algebra 1084 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 573
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 7 ], [ 5, 6 ], [ 6, 4 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 7, 6, 4 ]
[ 4, 7, 6 ]
[ 6, 4, 7 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 1 0 0 1 0)
(1 1 1 1 0 0 1 1)
(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 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 416 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 1110 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 583 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
vertex 6 -> Algebra 220 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 576
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 1 0 1 0 0)
(1 1 1 1 0 1 0 1)
(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 0 1 0 1 0 1)
Good mutations
vertex 1 -> Algebra 419 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 1112 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 600 permutation [ 2, 1, 4, 3, 6, 5, 7, 8 ]
vertex 7 -> Algebra 220 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 578
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 4 ], [ 6, 7 ], [ 8, 6 ]
Relations
[ 6, 4, 2 ]
[ 4, 5, 3 ]
[ 2, 6, 4 ]
[ 5, 3, 4 ]
[ 8, 6, 4 ]
[ 3, 4, 5 ]
[ 6, 4, 8 ]
[ 4, 2, 6 ] - [ 4, 8, 6 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 0 1 1 0)
(1 1 1 1 0 1 1 1)
(1 1 0 1 1 1 1 1)
(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 1 1 1)
Good mutations
vertex 1 -> Algebra 421 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 220 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 1115 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 7 -> Algebra 1112 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 583
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 2 ], [ 3, 8 ], [ 4, 3 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 7, 5 ], [ 8, 4 ]
Relations
[ 4, 3, 2 ]
[ 2, 4, 3 ]
[ 8, 4, 3 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 5, 4, 7 ]
[ 4, 3, 8 ]
[ 3, 2, 4 ] - [ 3, 8, 4 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 1 0 0 1 0)
(1 1 1 1 0 0 1 1)
(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 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 426 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 769 permutation [ 8, 2, 1, 4, 3, 5, 6, 7 ]
vertex 5 -> Algebra 226 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 573 permutation [ 1, 2, 3, 4, 6, 5, 7, 8 ]
Algebra 588
Quiver
[ 2, 1 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 4, 8 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 5 ]
Relations
[ 5, 4, 2 ]
[ 2, 5, 4 ]
[ 8, 5, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 5, 4, 8 ]
[ 4, 2, 5 ] - [ 4, 8, 5 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 1 0 1 0)
(1 1 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 0 0 0 1 0 1 1)
Good mutations
vertex 1 -> Algebra 431 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 552 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 4 -> Algebra 226 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 1123 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 600
Quiver
[ 1, 2 ], [ 1, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 8 ], [ 5, 3 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 3, 4, 1 ]
[ 1, 3, 4 ]
[ 8, 3, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 3, 4, 8 ]
[ 4, 1, 3 ] - [ 4, 8, 3 ]
Cartan matrix
(1 1 1 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(0 0 1 1 0 0 0 0)
(1 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 444 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 239 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 576 permutation [ 2, 1, 4, 3, 6, 5, 7, 8 ]
Algebra 607
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 7 ], [ 3, 8 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 0 0 0 1 1)
(1 1 1 1 1 0 0 1)
(1 1 1 0 1 1 0 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 451 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 1112 permutation [ 2, 1, 4, 5, 6, 3, 7, 8 ]
vertex 5 -> Algebra 239 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 1139 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 609
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 5 ], [ 4, 3 ], [ 5, 4 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 3 ]
Relations
[ 5, 4, 3 ]
[ 3, 5, 4 ]
[ 4, 3, 5 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
Cartan matrix
(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 0 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)
(1 1 1 0 1 0 1 1)
Good mutations
vertex 2 -> Algebra 453 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 1139 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 239 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 663
Quiver
[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 3 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ]
Relations
[ 8, 4, 1 ]
[ 8, 4, 3 ]
[ 1, 8, 4 ]
[ 3, 8, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 4, 1, 8 ] - [ 4, 3, 8 ]
Cartan matrix
(1 0 0 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 1)
(1 0 1 1 0 1 1 1)
(1 0 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 1 0 1 1 1)
Good mutations
vertex 2 -> Algebra 769 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 426 permutation [ 2, 3, 5, 4, 6, 7, 8, 1 ]
vertex 6 -> Algebra 946 permutation [ 2, 3, 5, 6, 4, 7, 8, 1 ]
vertex 7 -> Algebra 932 permutation [ 2, 3, 5, 4, 7, 6, 8, 1 ]
Algebra 669
Quiver
[ 1, 8 ], [ 2, 3 ], [ 3, 8 ], [ 4, 1 ], [ 4, 3 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 8, 4, 1 ]
[ 8, 4, 3 ]
[ 1, 8, 4 ]
[ 3, 8, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 1, 8 ] - [ 4, 3, 8 ]
Cartan matrix
(1 0 0 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 1)
(1 0 1 1 1 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 1 1 0 1 1)
Good mutations
vertex 2 -> Algebra 775 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 392 permutation [ 2, 3, 4, 6, 5, 7, 8, 1 ]
vertex 5 -> Algebra 908 permutation [ 2, 3, 5, 6, 4, 7, 8, 1 ]
Algebra 769
Quiver
[ 1, 8 ], [ 2, 3 ], [ 2, 8 ], [ 4, 1 ], [ 4, 2 ], [ 4, 6 ], [ 5, 4 ], [ 6, 5 ], [ 6, 7 ], [ 8, 4 ]
Relations
[ 8, 4, 1 ]
[ 8, 4, 2 ]
[ 1, 8, 4 ]
[ 2, 8, 4 ]
[ 6, 5, 4 ]
[ 4, 6, 5 ]
[ 5, 4, 6 ]
[ 4, 1, 8 ] - [ 4, 2, 8 ]
Cartan matrix
(1 0 0 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 1 1 1 0 1 1 1)
(1 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 1 0 1 1 1)
Good mutations
vertex 3 -> Algebra 663 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 583 permutation [ 3, 2, 5, 4, 6, 7, 8, 1 ]
vertex 6 -> Algebra 1123 permutation [ 3, 2, 5, 6, 4, 7, 8, 1 ]
vertex 7 -> Algebra 1110 permutation [ 3, 2, 5, 4, 7, 6, 8, 1 ]
Algebra 775
Quiver
[ 1, 8 ], [ 2, 3 ], [ 2, 8 ], [ 4, 1 ], [ 4, 2 ], [ 4, 5 ], [ 5, 7 ], [ 6, 5 ], [ 7, 6 ], [ 8, 4 ]
Relations
[ 8, 4, 1 ]
[ 8, 4, 2 ]
[ 1, 8, 4 ]
[ 2, 8, 4 ]
[ 7, 6, 5 ]
[ 5, 7, 6 ]
[ 6, 5, 7 ]
[ 4, 1, 8 ] - [ 4, 2, 8 ]
Cartan matrix
(1 0 0 0 0 0 0 1)
(0 1 1 0 0 0 0 1)
(0 0 1 0 0 0 0 0)
(1 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 1 1 0 1 1)
Good mutations
vertex 3 -> Algebra 669 permutation [ 1, 3, 2, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 549 permutation [ 3, 2, 4, 6, 5, 7, 8, 1 ]
vertex 5 -> Algebra 1084 permutation [ 3, 2, 5, 6, 4, 7, 8, 1 ]
Algebra 908
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 4 ], [ 3, 5 ], [ 5, 2 ], [ 5, 6 ], [ 5, 8 ], [ 6, 3 ], [ 7, 5 ], [ 8, 7 ]
Relations
[ 7, 5, 2 ]
[ 5, 6, 3 ]
[ 2, 7, 5 ]
[ 6, 3, 5 ]
[ 8, 7, 5 ]
[ 3, 5, 6 ]
[ 7, 5, 8 ]
[ 5, 2, 7 ] - [ 5, 8, 7 ]
Cartan matrix
(1 1 0 0 0 0 1 0)
(0 1 0 0 0 0 1 0)
(0 1 1 1 1 0 1 1)
(0 0 0 1 0 0 0 0)
(0 1 0 0 1 1 1 1)
(0 0 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 1084 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 669 permutation [ 8, 1, 2, 5, 3, 4, 6, 7 ]
vertex 4 -> Algebra 946 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 5 -> Algebra 395 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 932
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 7 ]
Relations
[ 7, 4, 2 ]
[ 4, 6, 3 ]
[ 2, 7, 4 ]
[ 6, 3, 4 ]
[ 8, 7, 4 ]
[ 3, 4, 6 ]
[ 7, 4, 8 ]
[ 4, 2, 7 ] - [ 4, 8, 7 ]
Cartan matrix
(1 1 0 0 0 0 1 0)
(0 1 0 0 0 0 1 0)
(0 1 1 1 0 0 1 1)
(0 1 0 1 0 1 1 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 1110 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 416 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 663 permutation [ 8, 1, 2, 4, 3, 6, 5, 7 ]
vertex 6 -> Algebra 937 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
Algebra 934
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 6 ]
Relations
[ 6, 4, 2 ]
[ 4, 5, 3 ]
[ 2, 6, 4 ]
[ 5, 3, 4 ]
[ 8, 6, 4 ]
[ 3, 4, 5 ]
[ 6, 4, 8 ]
[ 4, 2, 6 ] - [ 4, 8, 6 ]
Cartan matrix
(1 1 0 0 0 1 0 0)
(0 1 0 0 0 1 0 0)
(0 1 1 1 0 1 0 1)
(0 1 0 1 1 1 0 1)
(0 0 1 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 1 0 1)
Good mutations
vertex 1 -> Algebra 1112 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 419 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 451 permutation [ 1, 2, 6, 3, 4, 5, 7, 8 ]
vertex 7 -> Algebra 421 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 937
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]
Relations
[ 7, 6, 2 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 4, 5 ]
[ 2, 7, 6 ]
[ 8, 7, 6 ]
[ 7, 6, 8 ]
[ 6, 2, 7 ] - [ 6, 8, 7 ]
Cartan matrix
(1 1 0 0 0 0 1 0)
(0 1 0 0 0 0 1 0)
(0 1 1 1 0 1 1 1)
(0 1 0 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(0 1 0 0 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 1115 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 932 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 6 -> Algebra 421 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 946
Quiver
[ 1, 2 ], [ 2, 7 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 5 ], [ 8, 7 ]
Relations
[ 7, 5, 2 ]
[ 5, 6, 4 ]
[ 2, 7, 5 ]
[ 6, 4, 5 ]
[ 8, 7, 5 ]
[ 4, 5, 6 ]
[ 7, 5, 8 ]
[ 5, 2, 7 ] - [ 5, 8, 7 ]
Cartan matrix
(1 1 0 0 0 0 1 0)
(0 1 0 0 0 0 1 0)
(0 1 1 1 1 0 1 1)
(0 1 0 1 1 0 1 1)
(0 1 0 0 1 1 1 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 1123 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 908 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 4 -> Algebra 663 permutation [ 8, 1, 2, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 431 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 966
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 7 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(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 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 0 0 1 1 1 0)
(0 1 1 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 1139 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 2 -> Algebra 549 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 453 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 451 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1084
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 4 ], [ 3, 5 ], [ 5, 2 ], [ 5, 6 ], [ 5, 8 ], [ 6, 3 ], [ 7, 5 ], [ 8, 7 ]
Relations
[ 7, 5, 2 ]
[ 5, 6, 3 ]
[ 2, 7, 5 ]
[ 6, 3, 5 ]
[ 8, 7, 5 ]
[ 3, 5, 6 ]
[ 7, 5, 8 ]
[ 5, 2, 7 ] - [ 5, 8, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 0 0 1 0)
(1 1 1 1 1 0 1 1)
(0 0 0 1 0 0 0 0)
(1 1 0 0 1 1 1 1)
(0 0 1 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 908 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 775 permutation [ 8, 2, 1, 5, 3, 4, 6, 7 ]
vertex 4 -> Algebra 1123 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 5 -> Algebra 552 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1110
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 6, 3 ], [ 7, 4 ], [ 8, 7 ]
Relations
[ 7, 4, 2 ]
[ 4, 6, 3 ]
[ 2, 7, 4 ]
[ 6, 3, 4 ]
[ 8, 7, 4 ]
[ 3, 4, 6 ]
[ 7, 4, 8 ]
[ 4, 2, 7 ] - [ 4, 8, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 0 0 1 0)
(1 1 1 1 0 0 1 1)
(1 1 0 1 0 1 1 1)
(0 0 1 0 1 1 0 0)
(0 0 1 0 0 1 0 0)
(0 0 0 1 0 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 932 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 573 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 769 permutation [ 8, 2, 1, 4, 3, 6, 5, 7 ]
vertex 6 -> Algebra 1115 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
Algebra 1112
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 4, 8 ], [ 5, 3 ], [ 6, 4 ], [ 7, 6 ], [ 8, 6 ]
Relations
[ 6, 4, 2 ]
[ 4, 5, 3 ]
[ 2, 6, 4 ]
[ 5, 3, 4 ]
[ 8, 6, 4 ]
[ 3, 4, 5 ]
[ 6, 4, 8 ]
[ 4, 2, 6 ] - [ 4, 8, 6 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 0 1 0 0)
(1 1 1 1 0 1 0 1)
(1 1 0 1 1 1 0 1)
(0 0 1 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 1 0 1)
Good mutations
vertex 1 -> Algebra 934 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 576 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 6 -> Algebra 607 permutation [ 2, 1, 6, 3, 4, 5, 7, 8 ]
vertex 7 -> Algebra 578 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1115
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 5, 3 ], [ 6, 2 ], [ 6, 8 ], [ 7, 6 ], [ 8, 7 ]
Relations
[ 7, 6, 2 ]
[ 4, 5, 3 ]
[ 5, 3, 4 ]
[ 3, 4, 5 ]
[ 2, 7, 6 ]
[ 8, 7, 6 ]
[ 7, 6, 8 ]
[ 6, 2, 7 ] - [ 6, 8, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 0 0 1 0)
(1 1 1 1 0 1 1 1)
(1 1 0 1 1 1 1 1)
(0 0 1 0 1 0 0 0)
(1 1 0 0 0 1 1 1)
(0 0 0 0 0 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 937 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 4 -> Algebra 1110 permutation [ 1, 2, 3, 6, 5, 4, 7, 8 ]
vertex 6 -> Algebra 578 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1123
Quiver
[ 2, 1 ], [ 2, 7 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 7, 5 ], [ 8, 7 ]
Relations
[ 7, 5, 2 ]
[ 5, 6, 4 ]
[ 2, 7, 5 ]
[ 6, 4, 5 ]
[ 8, 7, 5 ]
[ 4, 5, 6 ]
[ 7, 5, 8 ]
[ 5, 2, 7 ] - [ 5, 8, 7 ]
Cartan matrix
(1 0 0 0 0 0 0 0)
(1 1 0 0 0 0 1 0)
(1 1 1 1 1 0 1 1)
(1 1 0 1 1 0 1 1)
(1 1 0 0 1 1 1 1)
(0 0 0 1 0 1 0 0)
(0 0 0 0 1 1 1 0)
(0 0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 946 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 3 -> Algebra 1084 permutation [ 1, 2, 4, 3, 5, 6, 7, 8 ]
vertex 4 -> Algebra 769 permutation [ 8, 2, 1, 5, 3, 4, 6, 7 ]
vertex 5 -> Algebra 588 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
Algebra 1139
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 7 ], [ 4, 5 ], [ 5, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 5 ], [ 8, 3 ]
Relations
[ 7, 5, 3 ]
[ 5, 6, 4 ]
[ 3, 7, 5 ]
[ 6, 4, 5 ]
[ 4, 5, 6 ]
[ 5, 3, 7 ]
Cartan matrix
(1 1 0 0 0 0 0 0)
(0 1 0 0 0 0 0 0)
(1 1 1 0 0 0 1 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)
(0 0 0 0 1 1 1 0)
(1 1 1 0 0 0 1 1)
Good mutations
vertex 2 -> Algebra 966 permutation [ 2, 1, 3, 4, 5, 6, 7, 8 ]
vertex 5 -> Algebra 609 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]
vertex 8 -> Algebra 607 permutation [ 1, 2, 3, 4, 5, 6, 7, 8 ]