Algebra 55

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 3, 5 ], [ 4, 5 ], [ 5, 6 ], [ 6, 3 ]

Relations

[ 6, 3, 2 ] 
[ 2, 6, 3 ] 
[ 5, 6, 3 ] 
[ 6, 3, 5 ] 
[ 3, 2, 6 ] - [ 3, 5, 6 ] 

Cartan matrix

(1 1 0 0 0 1)
(0 1 0 0 0 1)
(0 1 1 0 1 1)
(0 0 0 1 1 1)
(0 0 0 0 1 1)
(0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra   57    permutation [ 4, 5, 3, 2, 1, 6 ]
vertex  4 -> Algebra   57    permutation [ 1, 2, 3, 5, 4, 6 ]

Algebra 57

Quiver

[ 1, 2 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 6, 3 ]

Relations

[ 6, 3, 2 ] 
[ 2, 6, 3 ] 
[ 4, 6, 3 ] 
[ 6, 3, 4 ] 
[ 3, 2, 6 ] - [ 3, 4, 6 ] 

Cartan matrix

(1 1 0 0 0 1)
(0 1 0 0 0 1)
(0 1 1 1 1 1)
(0 0 0 1 1 1)
(0 0 0 0 1 0)
(0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra   64    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   55    permutation [ 1, 2, 3, 5, 4, 6 ]

Algebra 64

Quiver

[ 2, 1 ], [ 2, 6 ], [ 3, 2 ], [ 3, 4 ], [ 4, 5 ], [ 4, 6 ], [ 6, 3 ]

Relations

[ 6, 3, 2 ] 
[ 2, 6, 3 ] 
[ 4, 6, 3 ] 
[ 6, 3, 4 ] 
[ 3, 2, 6 ] - [ 3, 4, 6 ] 

Cartan matrix

(1 0 0 0 0 0)
(1 1 0 0 0 1)
(1 1 1 1 1 1)
(0 0 0 1 1 1)
(0 0 0 0 1 0)
(0 0 1 0 0 1)

Good mutations

vertex  1 -> Algebra   57    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   57    permutation [ 5, 4, 3, 2, 1, 6 ]