Algebra 224
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 7, 5, 2 ]
[ 4, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 7 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 5, 2, 3 ] - [ 5, 6, 3 ]
[ 2, 3, 5 ] - [ 2, 7, 5 ]
Cartan matrix
(1 1 1 0 1 0 1)
(0 1 1 0 1 0 1)
(0 1 1 1 1 0 0)
(0 1 0 1 0 0 1)
(0 1 1 0 1 1 0)
(0 0 1 1 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 282 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 378 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
Algebra 232
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 2 ]
Relations
[ 4, 3, 5, 6, 7, 2 ]
[ 5, 6, 7, 2, 4, 3 ]
[ 3, 5, 6, 7, 2, 4 ]
[ 6, 7, 2, 4, 3, 5 ]
[ 7, 2, 4, 3, 5, 6 ]
[ 2, 4, 3, 5, 6, 7 ]
Cartan matrix
(1 1 1 1 1 1 0)
(0 1 1 1 1 1 0)
(0 1 1 0 1 1 1)
(0 0 1 1 1 1 1)
(0 1 0 1 1 1 1)
(0 1 1 1 0 1 1)
(0 1 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 288 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 349 permutation [ 6, 1, 4, 7, 2, 3, 5 ]
Algebra 282
Quiver
[ 2, 1 ], [ 2, 3 ], [ 2, 7 ], [ 3, 4 ], [ 3, 5 ], [ 4, 2 ], [ 5, 2 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 7, 5, 2 ]
[ 4, 2, 3 ]
[ 2, 3, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 2, 7 ]
[ 3, 4, 2 ] - [ 3, 5, 2 ]
[ 5, 2, 3 ] - [ 5, 6, 3 ]
[ 2, 3, 5 ] - [ 2, 7, 5 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 0 1 0 1)
(1 1 1 1 1 0 0)
(1 1 0 1 0 0 1)
(1 1 1 0 1 1 0)
(0 0 1 1 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 224 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 398 permutation [ 3, 5, 4, 2, 7, 1, 6 ]
Algebra 288
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 5 ], [ 4, 3 ], [ 5, 6 ], [ 6, 7 ], [ 7, 2 ]
Relations
[ 4, 3, 5, 6, 7, 2 ]
[ 5, 6, 7, 2, 4, 3 ]
[ 3, 5, 6, 7, 2, 4 ]
[ 6, 7, 2, 4, 3, 5 ]
[ 7, 2, 4, 3, 5, 6 ]
[ 2, 4, 3, 5, 6, 7 ]
Cartan matrix
(1 0 0 0 0 0 0)
(1 1 1 1 1 1 0)
(1 1 1 0 1 1 1)
(0 0 1 1 1 1 1)
(1 1 0 1 1 1 1)
(1 1 1 1 0 1 1)
(1 1 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 232 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 339 permutation [ 1, 3, 5, 4, 6, 7, 2 ]
Algebra 339
Quiver
[ 1, 7 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 1 ], [ 6, 4 ], [ 7, 6 ]
Relations
[ 7, 6, 1 ]
[ 3, 5, 6, 4, 2 ]
[ 5, 6, 4, 2, 3 ]
[ 2, 3, 5, 6, 4 ]
[ 7, 6, 4 ]
[ 6, 4, 2, 3, 5 ]
[ 1, 7, 6 ]
[ 4, 2, 3, 5, 6 ] - [ 4, 7, 6 ]
[ 6, 1, 7 ] - [ 6, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 1)
(1 1 1 0 1 1 0)
(1 0 1 1 1 1 1)
(0 1 1 1 1 1 1)
(1 1 0 1 1 1 1)
(1 1 1 1 0 1 1)
(0 0 0 0 0 1 1)
Good mutations
vertex 1 -> Algebra 395 permutation [ 5, 4, 7, 6, 1, 2, 3 ]
vertex 4 -> Algebra 382 permutation [ 5, 2, 1, 6, 7, 4, 3 ]
vertex 5 -> Algebra 340 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex 7 -> Algebra 288 permutation [ 1, 7, 2, 4, 3, 5, 6 ]
Algebra 340
Quiver
[ 1, 7 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 4, 7 ], [ 5, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 7, 5, 1 ]
[ 3, 5, 4, 2 ]
[ 2, 3, 5, 4 ]
[ 7, 5, 4 ]
[ 1, 7, 5 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 5, 4, 2, 3 ] - [ 5, 6, 3 ]
[ 4, 2, 3, 5 ] - [ 4, 7, 5 ]
[ 5, 1, 7 ] - [ 5, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 1)
(1 1 1 0 1 0 0)
(1 0 1 1 1 0 1)
(0 1 1 1 1 0 1)
(1 1 1 1 1 1 1)
(0 0 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 414 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 2 -> Algebra 389 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 378 permutation [ 2, 5, 4, 6, 1, 7, 3 ]
vertex 6 -> Algebra 339 permutation [ 1, 2, 3, 4, 6, 5, 7 ]
Algebra 349
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 6, 7 ], [ 7, 1 ]
Relations
[ 4, 3, 6, 7, 1 ]
[ 3, 5, 2 ]
[ 6, 7, 1, 4, 3 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 7, 1, 4, 3, 6 ]
[ 1, 4, 3, 6, 7 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
[ 3, 5, 4 ] - [ 3, 6, 7, 1, 4 ]
Cartan matrix
(1 0 1 1 0 1 0)
(1 1 1 0 0 1 1)
(1 0 1 1 1 1 1)
(0 0 1 1 0 1 1)
(0 1 1 1 1 1 1)
(1 0 0 1 0 1 1)
(1 0 1 1 0 0 1)
Good mutations
vertex 2 -> Algebra 395 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 382 permutation [ 2, 4, 6, 3, 7, 1, 5 ]
vertex 5 -> Algebra 232 permutation [ 2, 5, 6, 3, 7, 1, 4 ]
vertex 6 -> Algebra 350 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 350
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 5 ], [ 3, 6 ], [ 4, 3 ], [ 5, 2 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 4, 3, 6, 1 ]
[ 3, 5, 2 ]
[ 2, 3, 5 ]
[ 4, 3, 5 ]
[ 1, 4, 3, 6 ]
[ 7, 3, 6 ]
[ 3, 6, 7 ]
[ 5, 2, 3 ] - [ 5, 4, 3 ]
[ 6, 1, 4, 3 ] - [ 6, 7, 3 ]
[ 3, 5, 4 ] - [ 3, 6, 1, 4 ]
Cartan matrix
(1 0 1 1 0 0 0)
(1 1 1 0 0 1 0)
(1 0 1 1 1 1 0)
(0 0 1 1 0 1 0)
(0 1 1 1 1 1 0)
(1 0 1 1 0 1 1)
(0 0 1 0 1 0 1)
Good mutations
vertex 1 -> Algebra 399 permutation [ 2, 5, 6, 3, 7, 4, 1 ]
vertex 2 -> Algebra 396 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 398 permutation [ 2, 4, 6, 3, 7, 1, 5 ]
vertex 7 -> Algebra 349 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 370
Quiver
[ 1, 3 ], [ 1, 7 ], [ 2, 5 ], [ 3, 5 ], [ 4, 7 ], [ 5, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 2 ], [ 6, 3 ], [ 7, 5 ]
Relations
[ 3, 5, 1 ]
[ 7, 5, 1 ]
[ 5, 6, 2 ]
[ 7, 5, 4 ]
[ 4, 7, 5 ]
[ 2, 5, 6 ]
[ 3, 5, 6 ]
[ 5, 1, 3 ] - [ 5, 6, 3 ]
[ 1, 3, 5 ] - [ 1, 7, 5 ]
[ 6, 2, 5 ] - [ 6, 3, 5 ]
[ 5, 1, 7 ] - [ 5, 4, 7 ]
Cartan matrix
(1 0 1 0 1 0 1)
(1 1 0 1 1 0 1)
(0 0 1 1 1 0 0)
(0 0 0 1 0 0 1)
(1 0 1 1 1 1 1)
(0 1 1 1 1 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 396 permutation [ 3, 5, 4, 1, 7, 6, 2 ]
vertex 2 -> Algebra 378 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex 3 -> Algebra 414 permutation [ 2, 1, 7, 3, 5, 4, 6 ]
vertex 4 -> Algebra 398 permutation [ 4, 1, 6, 5, 2, 3, 7 ]
Algebra 378
Quiver
[ 1, 3 ], [ 1, 7 ], [ 2, 1 ], [ 2, 4 ], [ 2, 5 ], [ 3, 2 ], [ 4, 7 ], [ 5, 6 ], [ 6, 3 ], [ 7, 2 ]
Relations
[ 3, 2, 1 ]
[ 7, 2, 1 ]
[ 4, 7, 2 ]
[ 5, 6, 3, 2 ]
[ 7, 2, 4 ]
[ 6, 3, 2, 5 ]
[ 3, 2, 5, 6 ]
[ 1, 3, 2 ] - [ 1, 7, 2 ]
[ 2, 1, 3 ] - [ 2, 5, 6, 3 ]
[ 2, 1, 7 ] - [ 2, 4, 7 ]
Cartan matrix
(1 1 1 0 1 0 1)
(1 1 1 1 1 1 1)
(0 1 1 1 1 0 0)
(0 0 0 1 0 0 1)
(0 0 1 0 1 1 0)
(0 1 1 1 0 1 0)
(0 1 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 395 permutation [ 3, 2, 4, 1, 7, 5, 6 ]
vertex 2 -> Algebra 224 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 3 -> Algebra 340 permutation [ 5, 1, 7, 3, 2, 4, 6 ]
vertex 4 -> Algebra 382 permutation [ 4, 1, 5, 2, 6, 3, 7 ]
vertex 5 -> Algebra 370 permutation [ 1, 5, 3, 4, 2, 6, 7 ]
Algebra 382
Quiver
[ 1, 4 ], [ 2, 6 ], [ 2, 7 ], [ 3, 5 ], [ 4, 2 ], [ 4, 3 ], [ 5, 6 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 4, 2, 7, 1 ]
[ 6, 4, 2 ]
[ 7, 1, 4, 2 ]
[ 5, 6, 4, 3 ]
[ 3, 5, 6, 4 ]
[ 6, 4, 3, 5 ]
[ 1, 4, 2, 7 ]
[ 2, 6, 4 ] - [ 2, 7, 1, 4 ]
[ 4, 2, 6 ] - [ 4, 3, 5, 6 ]
Cartan matrix
(1 1 1 1 1 1 0)
(1 1 1 1 0 1 1)
(0 0 1 0 1 1 0)
(0 1 1 1 1 1 1)
(0 0 0 1 1 1 0)
(0 0 1 1 0 1 0)
(1 0 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 378 permutation [ 2, 4, 6, 1, 3, 5, 7 ]
vertex 2 -> Algebra 349 permutation [ 6, 1, 4, 2, 7, 3, 5 ]
vertex 3 -> Algebra 398 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 339 permutation [ 3, 2, 7, 6, 1, 4, 5 ]
Algebra 389
Quiver
[ 1, 7 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 4, 2 ], [ 4, 7 ], [ 5, 1 ], [ 5, 4 ], [ 5, 6 ], [ 6, 2 ], [ 7, 5 ]
Relations
[ 7, 5, 1 ]
[ 3, 4, 2 ]
[ 4, 2, 3 ]
[ 7, 5, 4 ]
[ 1, 7, 5 ]
[ 6, 2, 5 ]
[ 2, 5, 6 ]
[ 5, 4, 2 ] - [ 5, 6, 2 ]
[ 2, 3, 4 ] - [ 2, 5, 4 ]
[ 4, 2, 5 ] - [ 4, 7, 5 ]
[ 5, 1, 7 ] - [ 5, 4, 7 ]
Cartan matrix
(1 0 0 0 0 0 1)
(1 1 1 1 1 0 1)
(0 0 1 1 0 0 1)
(0 1 0 1 1 0 1)
(1 1 0 1 1 1 1)
(0 1 1 0 0 1 0)
(0 0 0 0 1 1 1)
Good mutations
vertex 3 -> Algebra 340 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 414 permutation [ 2, 1, 7, 5, 4, 3, 6 ]
Algebra 395
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 6, 7 ], [ 7, 1 ]
Relations
[ 4, 2, 6, 7, 1 ]
[ 3, 5, 4, 2 ]
[ 6, 7, 1, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 4, 2, 3, 5 ]
[ 7, 1, 4, 2, 6 ]
[ 1, 4, 2, 6, 7 ]
[ 2, 3, 5, 4 ] - [ 2, 6, 7, 1, 4 ]
Cartan matrix
(1 1 1 1 0 1 0)
(1 1 1 1 1 1 1)
(0 0 1 1 1 0 0)
(0 1 1 1 0 1 1)
(0 1 0 1 1 1 1)
(1 0 0 1 0 1 1)
(1 1 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 414 permutation [ 5, 6, 7, 2, 4, 1, 3 ]
vertex 2 -> Algebra 398 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 3 -> Algebra 349 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 378 permutation [ 4, 2, 1, 3, 6, 7, 5 ]
vertex 5 -> Algebra 339 permutation [ 5, 6, 7, 2, 1, 4, 3 ]
vertex 6 -> Algebra 396 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 396
Quiver
[ 1, 4 ], [ 2, 3 ], [ 2, 6 ], [ 3, 5 ], [ 4, 2 ], [ 5, 4 ], [ 6, 1 ], [ 6, 7 ], [ 7, 2 ]
Relations
[ 4, 2, 6, 1 ]
[ 3, 5, 4, 2 ]
[ 5, 4, 2, 3 ]
[ 4, 2, 3, 5 ]
[ 1, 4, 2, 6 ]
[ 7, 2, 6 ]
[ 2, 6, 7 ]
[ 6, 1, 4, 2 ] - [ 6, 7, 2 ]
[ 2, 3, 5, 4 ] - [ 2, 6, 1, 4 ]
Cartan matrix
(1 1 1 1 0 0 0)
(1 1 1 1 1 1 0)
(0 0 1 1 1 0 0)
(0 1 1 1 0 1 0)
(0 1 0 1 1 1 0)
(1 1 1 1 0 1 1)
(0 1 1 0 1 0 1)
Good mutations
vertex 2 -> Algebra 399 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 3 -> Algebra 350 permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex 4 -> Algebra 370 permutation [ 4, 7, 1, 3, 2, 6, 5 ]
vertex 7 -> Algebra 395 permutation [ 1, 2, 3, 4, 5, 7, 6 ]
Algebra 398
Quiver
[ 1, 4 ], [ 2, 6 ], [ 2, 7 ], [ 3, 5 ], [ 3, 6 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 4 ], [ 7, 1 ]
Relations
[ 4, 2, 7, 1 ]
[ 6, 4, 2 ]
[ 7, 1, 4, 2 ]
[ 5, 4, 3 ]
[ 6, 4, 3 ]
[ 4, 3, 5 ]
[ 1, 4, 2, 7 ]
[ 2, 6, 4 ] - [ 2, 7, 1, 4 ]
[ 3, 5, 4 ] - [ 3, 6, 4 ]
[ 4, 2, 6 ] - [ 4, 3, 6 ]
Cartan matrix
(1 1 1 1 0 1 0)
(1 1 0 1 0 1 1)
(0 0 1 1 1 1 0)
(0 1 1 1 0 1 1)
(0 1 0 1 1 0 1)
(0 0 0 1 0 1 0)
(1 0 1 1 0 0 1)
Good mutations
vertex 1 -> Algebra 370 permutation [ 2, 5, 6, 1, 4, 3, 7 ]
vertex 2 -> Algebra 350 permutation [ 6, 1, 4, 2, 7, 3, 5 ]
vertex 4 -> Algebra 282 permutation [ 6, 4, 1, 3, 2, 7, 5 ]
vertex 5 -> Algebra 382 permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex 6 -> Algebra 395 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
Algebra 399
Quiver
[ 1, 4 ], [ 2, 1 ], [ 2, 6 ], [ 3, 5 ], [ 3, 6 ], [ 4, 2 ], [ 4, 3 ], [ 5, 4 ], [ 6, 4 ], [ 6, 7 ], [ 7, 3 ]
Relations
[ 4, 2, 1 ]
[ 1, 4, 2 ]
[ 6, 4, 2 ]
[ 5, 4, 3 ]
[ 4, 3, 5 ]
[ 7, 3, 6 ]
[ 3, 6, 7 ]
[ 6, 4, 3 ] - [ 6, 7, 3 ]
[ 2, 1, 4 ] - [ 2, 6, 4 ]
[ 3, 5, 4 ] - [ 3, 6, 4 ]
[ 4, 2, 6 ] - [ 4, 3, 6 ]
Cartan matrix
(1 0 1 1 0 0 0)
(1 1 1 1 0 1 1)
(0 0 1 1 1 1 0)
(0 1 1 1 0 1 0)
(0 1 0 1 1 0 0)
(0 0 1 1 0 1 1)
(0 0 1 0 1 0 1)
Good mutations
vertex 6 -> Algebra 396 permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex 7 -> Algebra 350 permutation [ 7, 1, 4, 6, 2, 3, 5 ]
Algebra 414
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 5 ], [ 4, 2 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 6, 3 ], [ 7, 1 ]
Relations
[ 5, 4, 7, 1 ]
[ 3, 5, 4, 2 ]
[ 2, 3, 5, 4 ]
[ 7, 1, 5, 4 ]
[ 6, 3, 5 ]
[ 3, 5, 6 ]
[ 1, 5, 4, 7 ]
[ 5, 4, 2, 3 ] - [ 5, 6, 3 ]
[ 4, 2, 3, 5 ] - [ 4, 7, 1, 5 ]
Cartan matrix
(1 1 1 1 1 1 0)
(0 1 1 0 1 0 0)
(0 0 1 1 1 0 1)
(1 1 1 1 1 0 1)
(0 1 1 1 1 1 1)
(0 0 1 0 0 1 0)
(1 0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 340 permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex 4 -> Algebra 370 permutation [ 2, 1, 4, 6, 5, 7, 3 ]
vertex 5 -> Algebra 389 permutation [ 2, 1, 6, 5, 4, 7, 3 ]
vertex 6 -> Algebra 395 permutation [ 6, 4, 7, 5, 1, 2, 3 ]