Algebra 1

Quiver

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

Relations

None 

Cartan matrix

(1 1 1 1 1 1)
(0 1 1 1 1 1)
(0 0 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  1 -> Algebra    2    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra    6    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra    7    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 2

Quiver

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

Relations

None 

Cartan matrix

(1 0 0 0 0 0)
(1 1 1 1 1 1)
(0 0 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  1 -> Algebra    1    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra    8    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   12    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 6

Quiver

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

Relations

None 

Cartan matrix

(1 1 1 1 0 1)
(0 1 1 1 0 1)
(0 0 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  1 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra    1    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 7

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   12    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra    1    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 8

Quiver

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

Relations

None 

Cartan matrix

(1 1 0 0 0 0)
(0 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  1 -> Algebra   13    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  2 -> Algebra    2    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  3 -> Algebra   28    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   29    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   30    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 11

Quiver

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

Relations

None 

Cartan matrix

(1 0 0 0 0 0)
(1 1 1 1 0 1)
(0 0 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  1 -> Algebra    6    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   29    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   36    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra    2    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   37    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 12

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra    7    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   30    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   37    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra    2    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 13

Quiver

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

Relations

None 

Cartan matrix

(1 1 0 0 0 0)
(0 1 0 0 0 0)
(1 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  2 -> Algebra    8    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  3 -> Algebra   38    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra    8    permutation [ 5, 4, 3, 1, 2, 6 ]
vertex  6 -> Algebra   39    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 23

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   25    permutation [ 4, 5, 3, 2, 1, 6 ]
vertex  4 -> Algebra   25    permutation [ 1, 2, 3, 5, 4, 6 ]
vertex  6 -> Algebra   56    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 25

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   36    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra    6    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   23    permutation [ 1, 2, 3, 5, 4, 6 ]
vertex  6 -> Algebra   28    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 26

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   37    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   28    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra    7    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra    6    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 28

Quiver

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

Relations

None 

Cartan matrix

(1 1 1 0 0 0)
(0 1 1 0 0 0)
(0 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  1 -> Algebra   38    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  3 -> Algebra    8    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   56    permutation [ 1, 2, 3, 5, 4, 6 ]
vertex  6 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 29

Quiver

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

Relations

None 

Cartan matrix

(1 1 0 0 0 0)
(0 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  1 -> Algebra    8    permutation [ 5, 4, 3, 2, 1, 6 ]
vertex  2 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  3 -> Algebra   56    permutation [ 1, 2, 3, 5, 4, 6 ]
vertex  4 -> Algebra   11    permutation [ 5, 4, 3, 2, 1, 6 ]
vertex  5 -> Algebra    8    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   59    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 30

Quiver

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

Relations

None 

Cartan matrix

(1 1 0 0 0 0)
(0 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  1 -> Algebra   39    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  2 -> Algebra   12    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   59    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra    8    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 36

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   25    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   11    permutation [ 5, 4, 3, 2, 1, 6 ]
vertex  4 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  5 -> Algebra   25    permutation [ 5, 4, 3, 2, 1, 6 ]
vertex  6 -> Algebra   38    permutation [ 2, 1, 3, 4, 5, 6 ]

Algebra 37

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   26    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  2 -> Algebra   59    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   38    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  5 -> Algebra   12    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   11    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 38

Quiver

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

Relations

None 

Cartan matrix

(1 1 1 0 0 0)
(0 1 0 0 0 0)
(0 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  1 -> Algebra   37    permutation [ 5, 4, 3, 1, 2, 6 ]
vertex  2 -> Algebra   28    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  3 -> Algebra   13    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   37    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  5 -> Algebra   28    permutation [ 5, 4, 3, 1, 2, 6 ]
vertex  6 -> Algebra   36    permutation [ 2, 1, 3, 4, 5, 6 ]

Algebra 39

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  2 -> Algebra   30    permutation [ 2, 1, 3, 4, 5, 6 ]
vertex  5 -> Algebra   30    permutation [ 5, 4, 3, 1, 2, 6 ]
vertex  6 -> Algebra   13    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 56

Quiver

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

Relations

None 

Cartan matrix

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

Good mutations

vertex  1 -> Algebra   28    permutation [ 4, 5, 3, 2, 1, 6 ]
vertex  3 -> Algebra   29    permutation [ 1, 2, 3, 5, 4, 6 ]
vertex  4 -> Algebra   28    permutation [ 1, 2, 3, 5, 4, 6 ]
vertex  6 -> Algebra   23    permutation [ 1, 2, 3, 4, 5, 6 ]

Algebra 59

Quiver

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

Relations

None 

Cartan matrix

(1 1 0 0 0 0)
(0 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  1 -> Algebra   30    permutation [ 5, 4, 3, 2, 1, 6 ]
vertex  2 -> Algebra   37    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  4 -> Algebra   37    permutation [ 5, 4, 3, 2, 1, 6 ]
vertex  5 -> Algebra   30    permutation [ 1, 2, 3, 4, 5, 6 ]
vertex  6 -> Algebra   29    permutation [ 1, 2, 3, 4, 5, 6 ]