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.
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 |
There are 416 cluster-tilted algebras of Dynkin type E7 which fall into 14 derived equivalence classes.
There are 1574 cluster-tilted algebras of Dynkin type E8 which fall into 15 derived equivalence classes.