The algebras derived equivalent to gentle cluster tilted algebras

TL;DR

This paper classifies all finite-dimensional algebras that are derived equivalent to gentle cluster tilted algebras, which are known to be of Dynkin type A or Euclidean type A˜.

Contribution

It provides a complete classification of algebras derived equivalent to gentle cluster tilted algebras, extending understanding of their derived categories.

Findings

Classification of all algebras derived equivalent to gentle cluster tilted algebras.

Identification of conditions under which these algebras are derived equivalent.

Extension of known results for cluster tilted algebras of specific types.

Abstract

A cluster tilted algebra is known to be gentle if and only if it is cluster tilted of Dynkin type $\bbA$ or Euclidean type $\tilde{\bbA}$. We classify all finite dimensional algebras which are derived equivalent to gentle cluster tilted algebras.