Algebra 3

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   14    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   16    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   17    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 4

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra    9    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   18    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 5

Quiver

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

Relations

[ 5, 4, 3 ] 
[ 3, 5, 4 ] 
[ 4, 3, 5 ] 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   10    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   24    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 9

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   31    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   33    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 10

Quiver

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

Relations

[ 5, 4, 3 ] 
[ 3, 5, 4 ] 
[ 4, 3, 5 ] 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra    5    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   16    permutation [ 4, 5, 3, 2, 1, 6 ]
vertex  6 -> Algebra   31    permutation [ 4, 3, 5, 2, 1, 6 ]

Algebra 14

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   18    permutation [ 1, 3, 2, 4, 5, 6 ]
vertex  3 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   41    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 16

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  3 -> Algebra   41    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   10    permutation [ 5, 4, 3, 1, 2, 6 ]
vertex  5 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   45    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 17

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  5 -> Algebra   45    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra    3    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 18

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  3 -> Algebra   14    permutation [ 1, 3, 2, 4, 5, 6 ]
vertex  5 -> Algebra   27    permutation [ 5, 4, 1, 2, 3, 6 ]

Algebra 20

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   33    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   27    permutation [ 5, 4, 1, 2, 3, 6 ]
vertex  5 -> Algebra    4    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 24

Quiver

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

Relations

[ 5, 4, 3 ] 
[ 3, 5, 4 ] 
[ 4, 3, 5 ] 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   31    permutation [ 4, 3, 5, 2, 1, 6 ]
vertex  3 -> Algebra   33    permutation [ 4, 3, 5, 2, 1, 6 ]
vertex  6 -> Algebra    5    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 27

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   18    permutation [ 3, 4, 5, 2, 1, 6 ]
vertex  4 -> Algebra   20    permutation [ 3, 4, 5, 2, 1, 6 ]
vertex  5 -> Algebra   41    permutation [ 3, 5, 4, 2, 1, 6 ]

Algebra 31

Quiver

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

Relations

[ 2, 3, 1 ] 
[ 3, 1, 2 ] 
[ 1, 2, 3 ] 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra    9    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   45    permutation [ 1, 3, 2, 4, 5, 6 ]
vertex  5 -> Algebra   24    permutation [ 5, 4, 2, 1, 3, 6 ]
vertex  6 -> Algebra   10    permutation [ 5, 4, 2, 1, 3, 6 ]

Algebra 33

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   20    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   24    permutation [ 5, 4, 2, 1, 3, 6 ]
vertex  5 -> Algebra    9    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 41

Quiver

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

Relations

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

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   27    permutation [ 5, 4, 1, 3, 2, 6 ]
vertex  3 -> Algebra   16    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   14    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 45

Quiver

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

Relations

[ 3, 2, 1 ] 
[ 1, 3, 2 ] 
[ 2, 1, 3 ] 

Cartan matrix

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

Good mutations

vertex  4 -> Algebra   31    permutation [ 1, 3, 2, 4, 5, 6 ]
vertex  5 -> Algebra   17    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   16    permutation [ 1, 2, 3, 4, 5, 6 ]