Derived equivalences for cluster-tilted algebras of Dynkin type D

Details Derived equivalences for cluster-tilted algebras of Dynkin type D Derived equivalences for cluster-tilted algebras of Dynkin type D

2010-12-21

arxiv.org/abs/1012.4661v1

Mathematics

Representation Theory

41 pages

Scientific paper

We provide a far reaching derived equivalence classification of cluster-tilted algebras of Dynkin type D. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with normal forms. We also suggest normal forms for the derived equivalence classes, but some subtle questions in the derived equivalence classification remain open.

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