Algebra 43
Quiver
[ 1, 5 ], [ 1, 6 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 4, 2 ], [ 4, 6 ], [ 5, 3 ], [ 6, 3 ]
Relations
[ 5, 3, 1 ]
[ 6, 3, 1 ]
[ 3, 4, 2 ]
[ 2, 3, 4 ]
[ 6, 3, 4 ]
[ 3, 1, 5 ]
[ 1, 5, 3 ] - [ 1, 6, 3 ]
[ 4, 2, 3 ] - [ 4, 6, 3 ]
[ 3, 1, 6 ] - [ 3, 4, 6 ]
Cartan matrix
(1 0 1 0 1 1)
(1 1 1 0 0 0)
(1 0 1 1 0 1)
(0 1 1 1 0 1)
(0 0 1 1 1 0)
(0 0 1 0 0 1)
Good mutations
vertex 2 -> Algebra 54 permutation [ 1, 3, 2, 4, 5, 6 ]
vertex 5 -> Algebra 54 permutation [ 4, 3, 5, 1, 2, 6 ]
vertex 6 -> Algebra 65 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 49
Quiver
[ 1, 2 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ]
Relations
[ 6, 3, 4, 5, 2 ]
[ 4, 5, 2, 6, 3 ]
[ 5, 2, 6, 3, 4 ]
[ 2, 6, 3, 4, 5 ]
[ 3, 4, 5, 2, 6 ]
Cartan matrix
(1 1 1 1 0 1)
(0 1 1 1 0 1)
(0 1 1 1 1 0)
(0 1 0 1 1 1)
(0 1 1 0 1 1)
(0 0 1 1 1 1)
Good mutations
vertex 1 -> Algebra 61 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 54 permutation [ 2, 6, 3, 4, 1, 5 ]
Algebra 54
Quiver
[ 1, 5 ], [ 1, 6 ], [ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 6 ], [ 5, 2 ], [ 6, 2 ]
Relations
[ 5, 2, 1 ]
[ 6, 2, 1 ]
[ 3, 4, 6, 2 ]
[ 4, 6, 2, 3 ]
[ 6, 2, 3, 4 ]
[ 2, 1, 5 ]
[ 1, 5, 2 ] - [ 1, 6, 2 ]
[ 2, 1, 6 ] - [ 2, 3, 4, 6 ]
Cartan matrix
(1 1 1 0 1 1)
(1 1 1 1 0 1)
(0 0 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 1 -> Algebra 49 permutation [ 5, 1, 3, 4, 6, 2 ]
vertex 3 -> Algebra 43 permutation [ 1, 3, 2, 4, 5, 6 ]
vertex 5 -> Algebra 65 permutation [ 3, 1, 6, 5, 4, 2 ]
vertex 6 -> Algebra 67 permutation [ 3, 1, 5, 2, 4, 6 ]
Algebra 61
Quiver
[ 2, 1 ], [ 2, 6 ], [ 3, 4 ], [ 4, 5 ], [ 5, 2 ], [ 6, 3 ]
Relations
[ 6, 3, 4, 5, 2 ]
[ 4, 5, 2, 6, 3 ]
[ 5, 2, 6, 3, 4 ]
[ 2, 6, 3, 4, 5 ]
[ 3, 4, 5, 2, 6 ]
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 1 0 1)
(1 1 1 1 1 0)
(1 1 0 1 1 1)
(1 1 1 0 1 1)
(0 0 1 1 1 1)
Good mutations
vertex 1 -> Algebra 49 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 67 permutation [ 1, 3, 4, 5, 2, 6 ]
Algebra 65
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 6 ], [ 4, 2 ], [ 5, 3 ], [ 6, 1 ], [ 6, 4 ]
Relations
[ 5, 3, 6, 1 ]
[ 3, 6, 4, 2 ]
[ 2, 3, 6, 4 ]
[ 3, 6, 1, 5 ]
[ 1, 5, 3, 6 ]
[ 4, 2, 3, 6 ]
[ 6, 1, 5, 3 ] - [ 6, 4, 2, 3 ]
Cartan matrix
(1 0 1 0 1 0)
(1 1 1 0 0 1)
(1 0 1 1 0 1)
(0 1 1 1 0 0)
(0 0 1 1 1 1)
(1 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 54 permutation [ 5, 6, 4, 2, 1, 3 ]
vertex 2 -> Algebra 67 permutation [ 2, 1, 5, 3, 4, 6 ]
vertex 3 -> Algebra 66 permutation [ 1, 2, 6, 4, 5, 3 ]
vertex 4 -> Algebra 54 permutation [ 2, 6, 1, 5, 4, 3 ]
vertex 5 -> Algebra 67 permutation [ 5, 4, 2, 3, 1, 6 ]
vertex 6 -> Algebra 43 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 66
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 1 ], [ 3, 4 ], [ 3, 6 ], [ 4, 2 ], [ 5, 3 ], [ 6, 2 ], [ 6, 5 ]
Relations
[ 5, 3, 1 ]
[ 1, 5, 3 ]
[ 4, 2, 3 ]
[ 2, 3, 4 ]
[ 2, 3, 6 ]
[ 5, 3, 6 ]
[ 3, 4, 2 ] - [ 3, 6, 2 ]
[ 6, 2, 3 ] - [ 6, 5, 3 ]
[ 3, 1, 5 ] - [ 3, 6, 5 ]
Cartan matrix
(1 0 0 0 1 0)
(1 1 1 0 0 0)
(1 1 1 1 1 1)
(0 1 0 1 0 0)
(0 0 1 1 1 0)
(0 1 1 0 1 1)
Good mutations
vertex 1 -> Algebra 67 permutation [ 4, 5, 1, 3, 2, 6 ]
vertex 4 -> Algebra 67 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 6 -> Algebra 65 permutation [ 1, 2, 6, 4, 5, 3 ]
Algebra 67
Quiver
[ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 6 ], [ 5, 4 ], [ 6, 2 ], [ 6, 5 ]
Relations
[ 5, 4, 1 ]
[ 3, 4, 6, 2 ]
[ 4, 6, 2, 3 ]
[ 1, 5, 4 ]
[ 2, 3, 4, 6 ]
[ 5, 4, 6 ]
[ 6, 2, 3, 4 ] - [ 6, 5, 4 ]
[ 4, 1, 5 ] - [ 4, 6, 5 ]
Cartan matrix
(1 0 0 0 1 0)
(1 1 1 1 0 0)
(1 0 1 1 1 1)
(1 1 0 1 1 1)
(0 0 0 1 1 0)
(0 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 65 permutation [ 2, 1, 4, 5, 3, 6 ]
vertex 3 -> Algebra 66 permutation [ 1, 2, 4, 3, 5, 6 ]
vertex 5 -> Algebra 61 permutation [ 1, 5, 2, 3, 4, 6 ]
vertex 6 -> Algebra 54 permutation [ 2, 4, 1, 5, 3, 6 ]