Algebra 18

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   67    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   71    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   72    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 19

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   64    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra   68    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra   73    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 24

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   44    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra   79    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 44

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   24    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  2 -> Algebra  126    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 64

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   79    permutation [ 1, 3, 2, 4, 5, 6, 7 ]
vertex  3 -> Algebra   19    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 67

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   18    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  189    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra  190    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 68

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   19    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  191    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 71

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  189    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra   73    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  6 -> Algebra   18    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 72

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  190    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  199    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  7 -> Algebra   18    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 73

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  191    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra   19    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra   71    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 79

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   24    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  3 -> Algebra   64    permutation [ 1, 3, 2, 4, 5, 6, 7 ]

Algebra 126

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   44    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  4 -> Algebra  199    permutation [ 1, 3, 2, 4, 6, 5, 7 ]
vertex  5 -> Algebra  190    permutation [ 1, 3, 2, 4, 6, 5, 7 ]

Algebra 189

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   71    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra  191    permutation [ 1, 2, 3, 4, 6, 5, 7 ]
vertex  6 -> Algebra   67    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 190

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   72    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  126    permutation [ 1, 3, 2, 4, 6, 5, 7 ]
vertex  7 -> Algebra   67    permutation [ 1, 2, 3, 4, 5, 6, 7 ]

Algebra 191

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   73    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  5 -> Algebra   68    permutation [ 1, 2, 3, 4, 5, 6, 7 ]
vertex  6 -> Algebra  189    permutation [ 1, 2, 3, 4, 6, 5, 7 ]

Algebra 199

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  4 -> Algebra  126    permutation [ 1, 3, 2, 4, 6, 5, 7 ]
vertex  6 -> Algebra   72    permutation [ 1, 2, 3, 4, 5, 6, 7 ]