Algebra 70

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  101    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  195    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  196    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 86

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  133    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  231    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  222    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra   88    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 88

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  135    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  234    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   86    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  179    permutation [ 5, 1, 2, 7, 4, 3, 6 ]

Algebra 101

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  251    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra   70    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  252    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  253    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  254    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 133

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   86    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  287    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  280    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  135    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 135

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   88    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  290    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  133    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  211    permutation [ 5, 2, 1, 7, 4, 3, 6 ]

Algebra 179

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  211    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  195    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  4 -> Algebra   88    permutation [ 2, 3, 6, 5, 1, 7, 4 ]
vertex  5 -> Algebra  181    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 181

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  213    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  200    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  179    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  333    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 185

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  338    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  188    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  4 -> Algebra  263    permutation [ 2, 5, 1, 4, 6, 7, 3 ]
vertex  7 -> Algebra  287    permutation [ 1, 6, 2, 4, 3, 5, 7 ]

Algebra 188

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  341    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  194    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  5 -> Algebra  185    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  229    permutation [ 3, 4, 1, 6, 7, 2, 5 ]
vertex  7 -> Algebra  290    permutation [ 1, 6, 2, 4, 3, 5, 7 ]

Algebra 194

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  345    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  252    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  188    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  4 -> Algebra   70    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  263    permutation [ 2, 4, 1, 3, 6, 7, 5 ]
vertex  6 -> Algebra  346    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  347    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 195

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  253    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  197    permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex  4 -> Algebra  346    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  179    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra   70    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 196

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  254    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  347    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   70    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 197

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  260    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  352    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  200    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  6 -> Algebra  195    permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex  7 -> Algebra  353    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 200

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  263    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  338    permutation [ 2, 1, 7, 4, 3, 5, 6 ]
vertex  5 -> Algebra  181    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  197    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  345    permutation [ 2, 1, 4, 3, 7, 5, 6 ]

Algebra 211

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  229    permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex  3 -> Algebra  179    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  135    permutation [ 3, 2, 6, 5, 1, 7, 4 ]
vertex  5 -> Algebra  213    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 213

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  234    permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex  3 -> Algebra  181    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  6 -> Algebra  211    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  361    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 222

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  280    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  376    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra   86    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  333    permutation [ 6, 1, 2, 7, 3, 4, 5 ]

Algebra 229

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  342    permutation [ 3, 6, 4, 2, 7, 1, 5 ]
vertex  2 -> Algebra  231    permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex  3 -> Algebra  253    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  4 -> Algebra  188    permutation [ 3, 6, 1, 2, 7, 4, 5 ]
vertex  5 -> Algebra  211    permutation [ 1, 5, 3, 4, 2, 6, 7 ]

Algebra 231

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  352    permutation [ 3, 2, 6, 4, 7, 1, 5 ]
vertex  2 -> Algebra   86    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  257    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  4 -> Algebra  346    permutation [ 3, 2, 4, 1, 7, 6, 5 ]
vertex  5 -> Algebra  234    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  6 -> Algebra  229    permutation [ 1, 6, 3, 4, 5, 2, 7 ]

Algebra 234

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  384    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra   88    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  263    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  5 -> Algebra  213    permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex  6 -> Algebra  231    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  346    permutation [ 5, 1, 4, 2, 7, 3, 6 ]

Algebra 237

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  385    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  387    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 251

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  101    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  387    permutation [ 2, 3, 5, 4, 1, 6, 7 ]
vertex  7 -> Algebra  392    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 252

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  194    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  101    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  380    permutation [ 1, 2, 4, 5, 3, 6, 7 ]
vertex  6 -> Algebra  376    permutation [ 4, 2, 1, 3, 7, 6, 5 ]
vertex  7 -> Algebra  368    permutation [ 4, 7, 1, 3, 6, 2, 5 ]

Algebra 253

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  394    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  257    permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex  3 -> Algebra  195    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  376    permutation [ 4, 2, 1, 3, 7, 6, 5 ]
vertex  5 -> Algebra  229    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  101    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 254

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  392    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  196    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  368    permutation [ 4, 7, 1, 3, 6, 2, 5 ]
vertex  7 -> Algebra  101    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 257

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  397    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  260    permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex  4 -> Algebra  280    permutation [ 6, 4, 1, 3, 7, 2, 5 ]
vertex  5 -> Algebra  231    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  253    permutation [ 1, 6, 3, 4, 5, 2, 7 ]

Algebra 260

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  400    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  197    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  287    permutation [ 3, 6, 1, 4, 7, 2, 5 ]
vertex  5 -> Algebra  263    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  6 -> Algebra  257    permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex  7 -> Algebra  347    permutation [ 3, 1, 4, 2, 7, 6, 5 ]

Algebra 263

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  401    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  200    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  185    permutation [ 3, 1, 7, 4, 2, 5, 6 ]
vertex  5 -> Algebra  234    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  260    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  194    permutation [ 3, 1, 4, 2, 7, 5, 6 ]

Algebra 280

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  222    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  257    permutation [ 3, 6, 4, 2, 7, 1, 5 ]
vertex  4 -> Algebra  133    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  361    permutation [ 6, 2, 1, 7, 3, 4, 5 ]

Algebra 287

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  352    permutation [ 3, 1, 6, 4, 7, 2, 5 ]
vertex  2 -> Algebra  133    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  260    permutation [ 3, 6, 1, 4, 7, 2, 5 ]
vertex  5 -> Algebra  290    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  185    permutation [ 1, 3, 5, 4, 6, 2, 7 ]

Algebra 290

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  384    permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  135    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  347    permutation [ 1, 3, 4, 5, 6, 2, 7 ]
vertex  6 -> Algebra  287    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  188    permutation [ 1, 3, 5, 4, 6, 2, 7 ]

Algebra 333

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  361    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  345    permutation [ 2, 1, 4, 5, 7, 3, 6 ]
vertex  4 -> Algebra  222    permutation [ 2, 3, 5, 6, 7, 1, 4 ]
vertex  7 -> Algebra  181    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 335

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  338    permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex  2 -> Algebra  385    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  7 -> Algebra  342    permutation [ 2, 5, 4, 1, 7, 6, 3 ]

Algebra 338

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  185    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  388    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra  341    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  4 -> Algebra  200    permutation [ 2, 1, 5, 4, 6, 7, 3 ]
vertex  5 -> Algebra  335    permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex  7 -> Algebra  352    permutation [ 2, 1, 5, 4, 7, 6, 3 ]

Algebra 341

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  188    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  380    permutation [ 3, 4, 1, 6, 7, 2, 5 ]
vertex  4 -> Algebra  345    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  5 -> Algebra  338    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  376    permutation [ 1, 4, 3, 7, 5, 2, 6 ]
vertex  7 -> Algebra  384    permutation [ 6, 1, 2, 4, 3, 5, 7 ]

Algebra 342

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  394    permutation [ 6, 4, 7, 3, 1, 2, 5 ]
vertex  4 -> Algebra  352    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  5 -> Algebra  335    permutation [ 4, 1, 7, 3, 2, 6, 5 ]
vertex  6 -> Algebra  229    permutation [ 6, 4, 1, 3, 7, 2, 5 ]

Algebra 345

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  341    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  5 -> Algebra  200    permutation [ 2, 1, 4, 3, 6, 7, 5 ]
vertex  6 -> Algebra  333    permutation [ 2, 1, 6, 3, 4, 7, 5 ]
vertex  7 -> Algebra  353    permutation [ 2, 1, 4, 3, 7, 6, 5 ]

Algebra 346

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  361    permutation [ 2, 1, 6, 3, 4, 7, 5 ]
vertex  2 -> Algebra  376    permutation [ 4, 3, 1, 2, 7, 6, 5 ]
vertex  3 -> Algebra  231    permutation [ 4, 2, 1, 3, 7, 6, 5 ]
vertex  4 -> Algebra  195    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  234    permutation [ 2, 4, 6, 3, 1, 7, 5 ]
vertex  6 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 347

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  353    permutation [ 2, 1, 4, 3, 7, 6, 5 ]
vertex  2 -> Algebra  368    permutation [ 4, 7, 1, 2, 6, 3, 5 ]
vertex  3 -> Algebra  290    permutation [ 1, 6, 2, 3, 4, 5, 7 ]
vertex  4 -> Algebra  196    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  260    permutation [ 2, 4, 1, 3, 7, 6, 5 ]
vertex  7 -> Algebra  194    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 352

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  397    permutation [ 6, 2, 7, 4, 1, 3, 5 ]
vertex  2 -> Algebra  287    permutation [ 2, 6, 1, 4, 7, 3, 5 ]
vertex  3 -> Algebra  342    permutation [ 1, 2, 4, 3, 5, 6, 7 ]
vertex  4 -> Algebra  197    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  338    permutation [ 2, 1, 7, 4, 3, 6, 5 ]
vertex  6 -> Algebra  231    permutation [ 6, 2, 1, 4, 7, 3, 5 ]
vertex  7 -> Algebra  384    permutation [ 6, 2, 1, 4, 3, 7, 5 ]

Algebra 353

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  347    permutation [ 2, 1, 4, 3, 7, 6, 5 ]
vertex  4 -> Algebra  384    permutation [ 6, 2, 1, 4, 3, 7, 5 ]
vertex  5 -> Algebra  345    permutation [ 2, 1, 4, 3, 7, 6, 5 ]
vertex  7 -> Algebra  197    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 361

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  346    permutation [ 2, 1, 4, 5, 7, 3, 6 ]
vertex  3 -> Algebra  333    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  4 -> Algebra  280    permutation [ 3, 2, 5, 6, 7, 1, 4 ]
vertex  7 -> Algebra  213    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 368

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  254    permutation [ 3, 6, 4, 1, 7, 5, 2 ]
vertex  2 -> Algebra  252    permutation [ 3, 6, 4, 1, 7, 5, 2 ]
vertex  4 -> Algebra  347    permutation [ 3, 4, 6, 1, 7, 5, 2 ]
vertex  7 -> Algebra  390    permutation [ 1, 3, 2, 6, 5, 7, 4 ]

Algebra 376

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  253    permutation [ 3, 2, 4, 1, 7, 6, 5 ]
vertex  2 -> Algebra  222    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  346    permutation [ 3, 4, 2, 1, 7, 6, 5 ]
vertex  6 -> Algebra  252    permutation [ 3, 2, 4, 1, 7, 6, 5 ]
vertex  7 -> Algebra  341    permutation [ 1, 6, 3, 2, 5, 7, 4 ]

Algebra 380

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  252    permutation [ 1, 2, 5, 3, 4, 6, 7 ]
vertex  5 -> Algebra  401    permutation [ 4, 3, 1, 2, 6, 7, 5 ]
vertex  6 -> Algebra  341    permutation [ 3, 6, 1, 2, 7, 4, 5 ]
vertex  7 -> Algebra  390    permutation [ 3, 1, 7, 2, 6, 4, 5 ]

Algebra 384

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  234    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  290    permutation [ 2, 1, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  401    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  4 -> Algebra  353    permutation [ 3, 2, 5, 4, 7, 1, 6 ]
vertex  6 -> Algebra  352    permutation [ 3, 2, 5, 4, 7, 1, 6 ]
vertex  7 -> Algebra  341    permutation [ 2, 3, 5, 4, 6, 1, 7 ]

Algebra 385

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  388    permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex  3 -> Algebra  335    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  5 -> Algebra  237    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  394    permutation [ 6, 1, 2, 4, 3, 5, 7 ]

Algebra 387

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  5 -> Algebra  394    permutation [ 6, 1, 2, 4, 3, 5, 7 ]
vertex  6 -> Algebra  251    permutation [ 5, 1, 2, 4, 3, 6, 7 ]
vertex  7 -> Algebra  237    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 388

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra  390    permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex  3 -> Algebra  338    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  5 -> Algebra  385    permutation [ 5, 2, 3, 4, 1, 6, 7 ]
vertex  7 -> Algebra  397    permutation [ 6, 1, 2, 4, 3, 5, 7 ]

Algebra 390

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra  380    permutation [ 2, 4, 1, 6, 7, 5, 3 ]
vertex  5 -> Algebra  388    permutation [ 1, 5, 3, 4, 2, 6, 7 ]
vertex  6 -> Algebra  368    permutation [ 1, 3, 2, 7, 5, 4, 6 ]
vertex  7 -> Algebra  400    permutation [ 6, 1, 2, 4, 3, 5, 7 ]

Algebra 392

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  254    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  251    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 394

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  253    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  397    permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex  5 -> Algebra  342    permutation [ 5, 6, 4, 2, 7, 1, 3 ]
vertex  6 -> Algebra  387    permutation [ 2, 3, 5, 4, 6, 1, 7 ]
vertex  7 -> Algebra  385    permutation [ 2, 3, 5, 4, 6, 1, 7 ]

Algebra 397

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  257    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra  400    permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex  5 -> Algebra  352    permutation [ 5, 2, 6, 4, 7, 1, 3 ]
vertex  6 -> Algebra  394    permutation [ 1, 6, 3, 4, 5, 2, 7 ]
vertex  7 -> Algebra  388    permutation [ 2, 3, 5, 4, 6, 1, 7 ]

Algebra 400

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  260    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  401    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  6 -> Algebra  397    permutation [ 1, 2, 6, 4, 5, 3, 7 ]
vertex  7 -> Algebra  390    permutation [ 2, 3, 5, 4, 6, 1, 7 ]

Algebra 401

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra  263    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  384    permutation [ 1, 2, 5, 4, 3, 6, 7 ]
vertex  6 -> Algebra  400    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  7 -> Algebra  380    permutation [ 3, 4, 2, 1, 7, 5, 6 ]