Algebra 1
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ]
Relations
None
Cartan matrix
(1 1 1 1 1 1)
(0 1 1 1 1 1)
(0 0 1 1 1 1)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 7 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 2
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 1 1 1)
(0 0 1 1 1 1)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 1 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 6
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 5, 4 ]
Relations
None
Cartan matrix
(1 1 1 1 0 1)
(0 1 1 1 0 1)
(0 0 1 1 0 1)
(0 0 0 1 0 0)
(0 0 0 1 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 25 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 1 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 7
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 1 1 1 0)
(0 1 1 1 1 0)
(0 0 1 1 1 0)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(0 0 1 1 1 1)
Good mutations
vertex 1 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 1 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 8
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0)
(0 1 0 0 0 0)
(0 1 1 1 1 1)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 13 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 2 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 3 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 29 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 30 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 11
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 3, 6 ], [ 5, 4 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 1 0 1)
(0 0 1 1 0 1)
(0 0 0 1 0 0)
(0 0 0 1 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 29 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 36 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 37 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 12
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 1 1 0)
(0 0 1 1 1 0)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(0 0 1 1 1 1)
Good mutations
vertex 1 -> Algebra 7 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 30 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 37 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 2 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 13
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 3, 6 ], [ 4, 5 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0)
(0 1 0 0 0 0)
(1 1 1 1 1 1)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 2 -> Algebra 8 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 3 -> Algebra 38 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 8 permutation [ 5, 4, 3, 1, 2, 6 ]
vertex 6 -> Algebra 39 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 23
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 4, 5 ], [ 5, 3 ]
Relations
None
Cartan matrix
(1 1 1 0 0 1)
(0 1 1 0 0 1)
(0 0 1 0 0 1)
(0 0 1 1 1 1)
(0 0 1 0 1 1)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 25 permutation [ 4, 5, 3, 2, 1, 6 ]
vertex 4 -> Algebra 25 permutation [ 1, 2, 3, 5, 4, 6 ]
vertex 6 -> Algebra 56 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 25
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ]
Relations
None
Cartan matrix
(1 1 1 0 0 1)
(0 1 1 0 0 1)
(0 0 1 0 0 1)
(0 0 1 1 1 1)
(0 0 0 0 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 36 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 23 permutation [ 1, 2, 3, 5, 4, 6 ]
vertex 6 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 26
Quiver
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 5, 4 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 1 1 0 0)
(0 1 1 1 0 0)
(0 0 1 1 0 0)
(0 0 0 1 0 0)
(0 0 0 1 1 0)
(0 0 1 1 0 1)
Good mutations
vertex 1 -> Algebra 37 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 28 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 7 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 6 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 28
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 3 ], [ 4, 5 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 1 0 0 0)
(0 1 1 0 0 0)
(0 0 1 0 0 0)
(0 0 1 1 1 0)
(0 0 0 0 1 0)
(0 0 1 0 0 1)
Good mutations
vertex 1 -> Algebra 38 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 3 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 56 permutation [ 1, 2, 3, 5, 4, 6 ]
vertex 6 -> Algebra 25 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 29
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 3, 6 ], [ 5, 4 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0)
(0 1 0 0 0 0)
(0 1 1 1 0 1)
(0 0 0 1 0 0)
(0 0 0 1 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 8 permutation [ 5, 4, 3, 2, 1, 6 ]
vertex 2 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 3 -> Algebra 56 permutation [ 1, 2, 3, 5, 4, 6 ]
vertex 4 -> Algebra 11 permutation [ 5, 4, 3, 2, 1, 6 ]
vertex 5 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 30
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0)
(0 1 0 0 0 0)
(0 1 1 1 1 0)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(0 1 1 1 1 1)
Good mutations
vertex 1 -> Algebra 39 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 2 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 8 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 36
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 6 ], [ 4, 3 ], [ 4, 5 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 0 0 1)
(0 0 1 0 0 1)
(0 0 1 1 1 1)
(0 0 0 0 1 0)
(0 0 0 0 0 1)
Good mutations
vertex 1 -> Algebra 25 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 11 permutation [ 5, 4, 3, 2, 1, 6 ]
vertex 4 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 5 -> Algebra 25 permutation [ 5, 4, 3, 2, 1, 6 ]
vertex 6 -> Algebra 38 permutation [ 2, 1, 3, 4, 5, 6 ]
Algebra 37
Quiver
[ 2, 1 ], [ 2, 3 ], [ 3, 4 ], [ 5, 4 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 0 0 0 0 0)
(1 1 1 1 0 0)
(0 0 1 1 0 0)
(0 0 0 1 0 0)
(0 0 0 1 1 0)
(0 0 1 1 0 1)
Good mutations
vertex 1 -> Algebra 26 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 2 -> Algebra 59 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 38 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 5 -> Algebra 12 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 11 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 38
Quiver
[ 1, 2 ], [ 1, 3 ], [ 4, 3 ], [ 4, 5 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 1 0 0 0)
(0 1 0 0 0 0)
(0 0 1 0 0 0)
(0 0 1 1 1 0)
(0 0 0 0 1 0)
(0 0 1 0 0 1)
Good mutations
vertex 1 -> Algebra 37 permutation [ 5, 4, 3, 1, 2, 6 ]
vertex 2 -> Algebra 28 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 3 -> Algebra 13 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 37 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 5 -> Algebra 28 permutation [ 5, 4, 3, 1, 2, 6 ]
vertex 6 -> Algebra 36 permutation [ 2, 1, 3, 4, 5, 6 ]
Algebra 39
Quiver
[ 1, 2 ], [ 3, 1 ], [ 3, 4 ], [ 4, 5 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0)
(0 1 0 0 0 0)
(1 1 1 1 1 0)
(0 0 0 1 1 0)
(0 0 0 0 1 0)
(1 1 1 1 1 1)
Good mutations
vertex 2 -> Algebra 30 permutation [ 2, 1, 3, 4, 5, 6 ]
vertex 5 -> Algebra 30 permutation [ 5, 4, 3, 1, 2, 6 ]
vertex 6 -> Algebra 13 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 56
Quiver
[ 1, 2 ], [ 2, 3 ], [ 4, 5 ], [ 5, 3 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 1 0 0 0)
(0 1 1 0 0 0)
(0 0 1 0 0 0)
(0 0 1 1 1 0)
(0 0 1 0 1 0)
(0 0 1 0 0 1)
Good mutations
vertex 1 -> Algebra 28 permutation [ 4, 5, 3, 2, 1, 6 ]
vertex 3 -> Algebra 29 permutation [ 1, 2, 3, 5, 4, 6 ]
vertex 4 -> Algebra 28 permutation [ 1, 2, 3, 5, 4, 6 ]
vertex 6 -> Algebra 23 permutation [ 1, 2, 3, 4, 5, 6 ]
Algebra 59
Quiver
[ 1, 2 ], [ 3, 2 ], [ 3, 4 ], [ 5, 4 ], [ 6, 3 ]
Relations
None
Cartan matrix
(1 1 0 0 0 0)
(0 1 0 0 0 0)
(0 1 1 1 0 0)
(0 0 0 1 0 0)
(0 0 0 1 1 0)
(0 1 1 1 0 1)
Good mutations
vertex 1 -> Algebra 30 permutation [ 5, 4, 3, 2, 1, 6 ]
vertex 2 -> Algebra 37 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 4 -> Algebra 37 permutation [ 5, 4, 3, 2, 1, 6 ]
vertex 5 -> Algebra 30 permutation [ 1, 2, 3, 4, 5, 6 ]
vertex 6 -> Algebra 29 permutation [ 1, 2, 3, 4, 5, 6 ]