Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D

TL;DR

This paper classifies cluster-tilted algebras of Dynkin type D up to derived equivalence, introduces a new notion called good mutation equivalence, and provides standard forms for these classes.

Contribution

It offers a comprehensive derived equivalence classification for these algebras and introduces a new, more tractable equivalence notion called good mutation equivalence.

Findings

Complete derived equivalence classification of cluster-tilted algebras of Dynkin type D.

Introduction of good mutation equivalence as a stronger, algorithmically manageable relation.

Provision of standard forms for each derived equivalence class.

Abstract

We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. 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 standard forms.