Algebra 19
Quiver
[ 1, 2 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 6, 3 ]
Relations
[ 5, 4, 2 ]
[ 6, 3, 4, 2 ]
[ 4, 2, 6, 3 ]
[ 4, 2, 5 ]
[ 3, 4, 2, 6 ]
[ 2, 5, 4 ] - [ 2, 6, 3, 4 ]
Cartan matrix
(1 1 1 1 1 1)
(0 1 1 1 1 1)
(0 1 1 1 0 0)
(0 1 0 1 0 1)
(0 0 0 1 1 0)
(0 0 1 1 0 1)
Good mutations
vertex 1 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 48 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 3 -> Algebra 22 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 6 -> Algebra 50 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 21
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ], [ 6, 2 ]
Relations
[ 4, 3, 6, 2 ]
[ 6, 2, 4, 3 ]
[ 3, 6, 2, 4 ]
[ 2, 4, 3, 6 ]
Cartan matrix
(1 1 1 1 1 0)
(0 1 1 1 1 0)
(0 1 1 0 0 1)
(0 0 1 1 1 1)
(0 0 0 0 1 0)
(0 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 34 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 53 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 50 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 52 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 22
Quiver
[ 1, 2 ], [ 2, 5 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 4, 6 ], [ 5, 3 ], [ 6, 3 ]
Relations
[ 5, 3, 2 ]
[ 6, 3, 2 ]
[ 4, 6, 3 ]
[ 6, 3, 4 ]
[ 3, 2, 5 ]
[ 2, 5, 3 ] - [ 2, 6, 3 ]
[ 3, 2, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 1 1 0 1 1)
(0 1 1 0 1 1)
(0 1 1 1 0 1)
(0 0 0 1 0 1)
(0 0 1 1 1 0)
(0 0 1 0 0 1)
Good mutations
vertex 1 -> Algebra 35 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 19 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 5 -> Algebra 40 permutation [ 3, 1, 2, 6, 4, 5 ]
vertex 6 -> Algebra 42 permutation [ 3, 1, 2, 6, 4, 5 ]
Algebra 32
Quiver
[ 2, 1 ], [ 2, 5 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 5, 4 ], [ 6, 3 ]
Relations
[ 5, 4, 2 ]
[ 6, 3, 4, 2 ]
[ 4, 2, 6, 3 ]
[ 4, 2, 5 ]
[ 3, 4, 2, 6 ]
[ 2, 5, 4 ] - [ 2, 6, 3, 4 ]
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 1 1 1)
(1 1 1 1 0 0)
(1 1 0 1 0 1)
(0 0 0 1 1 0)
(0 0 1 1 0 1)
Good mutations
vertex 1 -> Algebra 19 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 60 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 3 -> Algebra 35 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 6 -> Algebra 53 permutation [ 6, 3, 5, 2, 1, 4 ]
Algebra 34
Quiver
[ 2, 1 ], [ 2, 4 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ], [ 6, 2 ]
Relations
[ 4, 3, 6, 2 ]
[ 6, 2, 4, 3 ]
[ 3, 6, 2, 4 ]
[ 2, 4, 3, 6 ]
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 1 1 0)
(1 1 1 0 0 1)
(0 0 1 1 1 1)
(0 0 0 0 1 0)
(1 1 0 1 1 1)
Good mutations
vertex 1 -> Algebra 21 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 35 permutation [ 5, 4, 6, 1, 3, 2 ]
vertex 4 -> Algebra 53 permutation [ 6, 3, 5, 2, 1, 4 ]
vertex 5 -> Algebra 42 permutation [ 6, 5, 4, 2, 1, 3 ]
Algebra 35
Quiver
[ 2, 1 ], [ 2, 5 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 4, 6 ], [ 5, 3 ], [ 6, 3 ]
Relations
[ 5, 3, 2 ]
[ 6, 3, 2 ]
[ 4, 6, 3 ]
[ 6, 3, 4 ]
[ 3, 2, 5 ]
[ 2, 5, 3 ] - [ 2, 6, 3 ]
[ 3, 2, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 0 1 1)
(1 1 1 1 0 1)
(0 0 0 1 0 1)
(0 0 1 1 1 0)
(0 0 1 0 0 1)
Good mutations
vertex 1 -> Algebra 22 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 63 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 32 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 5 -> Algebra 47 permutation [ 3, 2, 1, 6, 4, 5 ]
vertex 6 -> Algebra 34 permutation [ 4, 6, 5, 2, 1, 3 ]
Algebra 40
Quiver
[ 1, 5 ], [ 1, 6 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 5, 4 ], [ 6, 3 ]
Relations
[ 5, 4, 1 ]
[ 6, 3, 4, 1 ]
[ 4, 1, 6, 3 ]
[ 4, 1, 5 ]
[ 3, 4, 1, 6 ]
[ 1, 5, 4 ] - [ 1, 6, 3, 4 ]
Cartan matrix
(1 0 1 1 1 1)
(1 1 1 1 0 0)
(1 0 1 1 0 0)
(1 0 0 1 0 1)
(0 0 0 1 1 0)
(0 0 1 1 0 1)
Good mutations
vertex 2 -> Algebra 47 permutation [ 1, 3, 2, 4, 5, 6 ]
vertex 6 -> Algebra 22 permutation [ 2, 3, 1, 5, 6, 4 ]
Algebra 42
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ], [ 6, 1 ]
Relations
[ 4, 3, 6, 1 ]
[ 6, 1, 4, 3 ]
[ 3, 6, 1, 4 ]
[ 1, 4, 3, 6 ]
Cartan matrix
(1 0 1 1 1 0)
(1 1 1 0 0 1)
(1 0 1 0 0 1)
(0 0 1 1 1 1)
(0 0 0 0 1 0)
(1 0 0 1 1 1)
Good mutations
vertex 2 -> Algebra 34 permutation [ 5, 4, 6, 3, 2, 1 ]
vertex 3 -> Algebra 46 permutation [ 1, 2, 6, 4, 5, 3 ]
vertex 4 -> Algebra 22 permutation [ 2, 3, 1, 5, 6, 4 ]
vertex 5 -> Algebra 52 permutation [ 5, 4, 6, 3, 2, 1 ]
Algebra 46
Quiver
[ 1, 4 ], [ 2, 3 ], [ 3, 1 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ], [ 6, 2 ], [ 6, 4 ]
Relations
[ 4, 3, 1 ]
[ 3, 6, 2 ]
[ 1, 4, 3 ]
[ 2, 3, 6 ]
[ 4, 3, 6 ]
[ 6, 2, 3 ] - [ 6, 4, 3 ]
[ 3, 1, 4 ] - [ 3, 6, 4 ]
Cartan matrix
(1 0 0 1 1 0)
(1 1 1 0 0 0)
(1 0 1 1 1 1)
(0 0 1 1 1 0)
(0 0 0 0 1 0)
(0 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 62 permutation [ 5, 4, 3, 6, 2, 1 ]
vertex 2 -> Algebra 58 permutation [ 1, 3, 2, 4, 5, 6 ]
vertex 5 -> Algebra 60 permutation [ 1, 4, 2, 3, 5, 6 ]
vertex 6 -> Algebra 42 permutation [ 1, 2, 6, 4, 5, 3 ]
Algebra 47
Quiver
[ 1, 5 ], [ 1, 6 ], [ 2, 3 ], [ 2, 4 ], [ 4, 1 ], [ 5, 4 ], [ 6, 2 ]
Relations
[ 5, 4, 1 ]
[ 6, 2, 4, 1 ]
[ 4, 1, 6, 2 ]
[ 4, 1, 5 ]
[ 2, 4, 1, 6 ]
[ 1, 5, 4 ] - [ 1, 6, 2, 4 ]
Cartan matrix
(1 1 1 1 1 1)
(1 1 1 1 0 0)
(0 0 1 0 0 0)
(1 0 0 1 0 1)
(0 0 0 1 1 0)
(0 1 1 1 0 1)
Good mutations
vertex 2 -> Algebra 48 permutation [ 1, 4, 3, 2, 5, 6 ]
vertex 3 -> Algebra 40 permutation [ 1, 3, 2, 4, 5, 6 ]
vertex 6 -> Algebra 35 permutation [ 3, 2, 1, 5, 6, 4 ]
Algebra 48
Quiver
[ 1, 5 ], [ 1, 6 ], [ 2, 1 ], [ 2, 4 ], [ 3, 4 ], [ 4, 6 ], [ 5, 2 ], [ 6, 2 ], [ 6, 3 ]
Relations
[ 5, 2, 1 ]
[ 6, 2, 1 ]
[ 4, 6, 2 ]
[ 4, 6, 3 ]
[ 2, 1, 5 ]
[ 3, 4, 6 ]
[ 1, 5, 2 ] - [ 1, 6, 2 ]
[ 6, 2, 4 ] - [ 6, 3, 4 ]
[ 2, 1, 6 ] - [ 2, 4, 6 ]
Cartan matrix
(1 1 1 1 1 1)
(1 1 0 1 0 1)
(0 0 1 1 0 0)
(0 0 0 1 0 1)
(0 1 0 1 1 0)
(0 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 51 permutation [ 5, 1, 4, 6, 3, 2 ]
vertex 2 -> Algebra 19 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 47 permutation [ 1, 4, 3, 2, 5, 6 ]
vertex 6 -> Algebra 58 permutation [ 3, 1, 5, 6, 4, 2 ]
Algebra 50
Quiver
[ 1, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 5, 4 ], [ 6, 2 ]
Relations
[ 5, 4, 2 ]
[ 4, 2, 3 ]
[ 6, 2, 3 ]
[ 4, 2, 5 ]
[ 2, 3, 6 ]
[ 3, 4, 2 ] - [ 3, 6, 2 ]
[ 2, 3, 4 ] - [ 2, 5, 4 ]
Cartan matrix
(1 1 1 1 1 0)
(0 1 1 1 1 0)
(0 1 1 1 0 1)
(0 1 0 1 0 0)
(0 0 0 1 1 0)
(0 1 0 0 1 1)
Good mutations
vertex 1 -> Algebra 53 permutation [ 6, 3, 5, 2, 1, 4 ]
vertex 2 -> Algebra 53 permutation [ 3, 1, 6, 2, 4, 5 ]
vertex 3 -> Algebra 52 permutation [ 6, 3, 5, 2, 1, 4 ]
vertex 4 -> Algebra 21 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 63 permutation [ 6, 2, 3, 4, 1, 5 ]
vertex 6 -> Algebra 19 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 51
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 3 ]
Relations
[ 6, 3, 4, 2 ]
[ 2, 6, 3, 4 ]
[ 5, 3, 4 ]
[ 3, 4, 5 ]
[ 3, 4, 2, 6 ]
[ 4, 2, 6, 3 ] - [ 4, 5, 3 ]
Cartan matrix
(1 1 1 0 0 1)
(0 1 1 0 0 1)
(0 1 1 1 0 0)
(0 1 1 1 1 1)
(0 0 1 0 1 0)
(0 0 1 1 0 1)
Good mutations
vertex 1 -> Algebra 62 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 48 permutation [ 2, 6, 5, 3, 1, 4 ]
vertex 6 -> Algebra 60 permutation [ 6, 2, 5, 3, 1, 4 ]
Algebra 52
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 6 ], [ 4, 3 ], [ 5, 4 ], [ 6, 2 ]
Relations
[ 4, 3, 6, 2 ]
[ 6, 2, 4, 3 ]
[ 3, 6, 2, 4 ]
[ 2, 4, 3, 6 ]
Cartan matrix
(1 1 1 1 0 0)
(0 1 1 1 0 0)
(0 1 1 0 0 1)
(0 0 1 1 0 1)
(0 0 1 1 1 1)
(0 1 0 1 0 1)
Good mutations
vertex 1 -> Algebra 42 permutation [ 6, 5, 4, 2, 1, 3 ]
vertex 2 -> Algebra 50 permutation [ 5, 4, 2, 6, 3, 1 ]
vertex 4 -> Algebra 60 permutation [ 6, 2, 5, 3, 1, 4 ]
vertex 5 -> Algebra 21 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 53
Quiver
[ 1, 4 ], [ 2, 1 ], [ 2, 6 ], [ 3, 6 ], [ 4, 2 ], [ 4, 3 ], [ 4, 5 ], [ 6, 4 ]
Relations
[ 4, 2, 1 ]
[ 1, 4, 2 ]
[ 6, 4, 2 ]
[ 6, 4, 3 ]
[ 3, 6, 4 ]
[ 2, 1, 4 ] - [ 2, 6, 4 ]
[ 4, 2, 6 ] - [ 4, 3, 6 ]
Cartan matrix
(1 0 1 1 1 0)
(1 1 0 1 1 1)
(0 0 1 0 0 1)
(0 1 1 1 1 1)
(0 0 0 0 1 0)
(0 0 0 1 1 1)
Good mutations
vertex 1 -> Algebra 32 permutation [ 5, 4, 2, 6, 3, 1 ]
vertex 2 -> Algebra 21 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 3 -> Algebra 58 permutation [ 1, 2, 6, 4, 5, 3 ]
vertex 4 -> Algebra 50 permutation [ 2, 4, 1, 5, 6, 3 ]
vertex 5 -> Algebra 50 permutation [ 5, 4, 2, 6, 3, 1 ]
vertex 6 -> Algebra 34 permutation [ 5, 4, 2, 6, 3, 1 ]
Algebra 58
Quiver
[ 1, 4 ], [ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 4, 2 ], [ 4, 5 ], [ 6, 4 ]
Relations
[ 4, 2, 1 ]
[ 1, 4, 2 ]
[ 3, 6, 4, 2 ]
[ 6, 4, 2, 3 ]
[ 4, 2, 3, 6 ]
[ 2, 1, 4 ] - [ 2, 3, 6, 4 ]
Cartan matrix
(1 0 0 1 1 0)
(1 1 1 1 1 1)
(0 0 1 1 1 1)
(0 1 1 1 1 0)
(0 0 0 0 1 0)
(0 1 0 1 1 1)
Good mutations
vertex 3 -> Algebra 46 permutation [ 1, 3, 2, 4, 5, 6 ]
vertex 4 -> Algebra 48 permutation [ 2, 6, 1, 5, 3, 4 ]
vertex 5 -> Algebra 63 permutation [ 1, 4, 2, 3, 5, 6 ]
vertex 6 -> Algebra 53 permutation [ 1, 2, 6, 4, 5, 3 ]
Algebra 60
Quiver
[ 1, 2 ], [ 2, 4 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 5, 2 ], [ 6, 2 ], [ 6, 3 ]
Relations
[ 2, 4, 1 ]
[ 4, 6, 3 ]
[ 1, 2, 4 ]
[ 2, 4, 6 ]
[ 3, 4, 6 ]
[ 4, 1, 2 ] - [ 4, 6, 2 ]
[ 6, 2, 4 ] - [ 6, 3, 4 ]
Cartan matrix
(1 1 0 0 0 0)
(0 1 0 1 0 0)
(1 0 1 1 0 0)
(1 1 0 1 0 1)
(0 1 0 1 1 0)
(0 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 51 permutation [ 5, 2, 4, 6, 3, 1 ]
vertex 2 -> Algebra 32 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 3 -> Algebra 63 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 5 -> Algebra 46 permutation [ 1, 3, 4, 2, 5, 6 ]
vertex 6 -> Algebra 52 permutation [ 5, 2, 4, 6, 3, 1 ]
Algebra 62
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 2 ], [ 4, 5 ], [ 5, 3 ], [ 6, 3 ]
Relations
[ 6, 3, 4, 2 ]
[ 2, 6, 3, 4 ]
[ 5, 3, 4 ]
[ 3, 4, 5 ]
[ 3, 4, 2, 6 ]
[ 4, 2, 6, 3 ] - [ 4, 5, 3 ]
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 0 0 1)
(1 1 1 1 0 0)
(1 1 1 1 1 1)
(0 0 1 0 1 0)
(0 0 1 1 0 1)
Good mutations
vertex 1 -> Algebra 51 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 46 permutation [ 6, 5, 3, 2, 1, 4 ]
Algebra 63
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 6 ], [ 5, 2 ], [ 6, 2 ]
Relations
[ 2, 3, 1 ]
[ 1, 2, 3 ]
[ 4, 6, 2, 3 ]
[ 6, 2, 3, 4 ]
[ 2, 3, 4, 6 ]
[ 3, 1, 2 ] - [ 3, 4, 6, 2 ]
Cartan matrix
(1 1 0 0 0 0)
(0 1 1 1 0 0)
(1 1 1 1 0 1)
(0 1 0 1 0 1)
(0 1 1 1 1 0)
(0 1 1 0 0 1)
Good mutations
vertex 2 -> Algebra 35 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 60 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 5 -> Algebra 58 permutation [ 1, 3, 4, 2, 5, 6 ]
vertex 6 -> Algebra 50 permutation [ 5, 2, 3, 4, 6, 1 ]