Derived equivalence classification of m-cluster tilted algebras of type A

TL;DR

This paper classifies m-cluster tilted algebras of type A up to derived equivalence by leveraging the combinatorics of the m-cluster complex, extending previous results in the field.

Contribution

It introduces a new classification method for m-cluster tilted algebras of type A using tilting complexes linked to the m-cluster complex's combinatorics.

Findings

Classification of connected components up to derived equivalence

Description of m-cluster tilted algebras as quivers with relations

Generalization of previous classification results

Abstract

We use the maximal faces of the $m$-cluster complex of type A to describe the m-cluster tilted algebras of type A as quivers with relations. We then classify connected components of m-cluster tilted algebras of type A up to derived equivalence using tilting complexes directly related to the combinatorics of the m-cluster complex of type A. This generalizes a result of Buan and Vatne.