Algebra 416

Quiver

[ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ], [ 4, 7 ], [ 5, 4 ], [ 5, 6 ], [ 6, 1 ], [ 7, 5 ]

Relations

[ 2, 3, 4, 1 ] 
[ 3, 4, 1, 2 ] 
[ 4, 1, 2, 3 ] 
[ 7, 5, 4 ] 
[ 6, 1, 5 ] 
[ 1, 5, 6 ] 
[ 5, 4, 7 ] 
[ 5, 4, 1 ] - [ 5, 6, 1 ] 
[ 1, 2, 3, 4 ] - [ 1, 5, 4 ] 
[ 4, 1, 5 ] - [ 4, 7, 5 ] 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  416    permutation [ 4, 7, 5, 1, 2, 3, 6 ]
vertex  4 -> Algebra  416    permutation [ 4, 5, 6, 1, 3, 7, 2 ]