# Cluster-tilted algebras of Dynkin type E

This page contains supplementary material to the paper Derived equivalence classification of cluster-tilted algebras of Dynkin type E by Janine Bastian, Thorsten Holm and Sefi Ladkani.

The derived equivalence classes of the cluster-tilted algebras of Dynkin type E are characterized by their so-called associated polynomials.

In the tables below, click on a polynomial to see the list of cluster-tilted algebras belonging to the corresponding class. For each algebra we write its quiver, defining relations, Cartan matrix and the complete list of good mutations.

## Type E6

There are 67 cluster-tilted algebras of Dynkin type E6 which fall into 6 derived equivalence classes.

Associated polynomial Size
x6 - x5 + x3 - x + 1 20
2( x6 - 2x4 + 4x3 - 2x2 + 1) 3
2( x6 - x4 + 2x3 - x2 + 1) 16
3( x6 + x3 + 1) 19
4( x6 + x4 + x2 + 1) 7
4( x6 + x5 - x4 + 2x3 - x2 + x + 1) 2

## Type E7

There are 416 cluster-tilted algebras of Dynkin type E7 which fall into 14 derived equivalence classes.

Associated polynomial Size
x7 - x6 + x4 - x3 + x - 1 64
2( x7 - 2x5 + 4x4 - 4x3 + 2x2 - 1) 8
2( x7 - x5 + x4 - x3 + x2 - 1) 72
2( x7 - x5 + 2x4 - 2x3 + x2 - 1) 32
3( x7 - 1) 124
4( x7 + x5 - 2x4 + 2x3 - x2 - 1) 8
4( x7 + x5 - x4 + x3 - x2 - 1) 56
4( x7 + x6 - 2x5 + 2x4 - 2x3 + 2x2 - x - 1) 2
4( x7 + x6 - x5 - x4 + x3 + x2 - x - 1) 4
4( x7 + x6 - x5 + x4 - x3 + x2 - x - 1) 16
5( x7 + x5 - x4 + x3 - x2 - 1) 17
6( x7 + x5 - x2 - 1) 1
6( x7 + x6 - x4 + x3 - x - 1) 11
8( x7 + x6 + x5 - x4 + x3 - x2 - x - 1) 1

## Type E8

There are 1574 cluster-tilted algebras of Dynkin type E8 which fall into 15 derived equivalence classes.

Associated polynomial Size
x8 - x7 + x5 - x4 + x3 - x + 1 128
2( x8 - 2x6 + 4x5 - 4x4 + 4x3 - 2x2 + 1) 16
2( x8 - x6 + x5 + x3 - x2 + 1) 256
2( x8 - x6 + 2x5 - 2x4 + 2x3 - x2 + 1) 64
3( x8 + x4 + 1) 384
4( x8 + x6 - 2x5 + 4x4 - 2x3 + x2 + 1) 22
4( x8 + x6 - x5 + 2x4 - x3 + x2 + 1) 221
4( x8 + x7 - 2x6 + 2x5 + 2x3 - 2x2 + x + 1) 12
4( x8 + x7 - x6 + 2x4 - x2 + x + 1) 48
4( x8 + x7 - x6 + x5 + x3 - x2 + x + 1) 72
5( x8 + x6 + x4 + x2 + 1) 167
6( x8 + x6 + x5 + x3 + x2 + 1) 38
6( x8 + x7 + 2x4 + x + 1) 118
8( x8 + x7 + x6 + 2x4 + x2 + x + 1) 24
8( x8 + 2x7 + 2x4 + 2x + 1) 4