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 ]