Mutation classes of \tilde{A}_n-quivers and derived equivalence classification of cluster tilted algebras of type \tilde{A}_n

TL;DR

This paper classifies mutation classes of ilde{A}_n quivers and provides a complete derived equivalence classification of cluster tilted algebras of this type, linking algebraic properties to combinatorial parameters.

Contribution

It offers an explicit description of mutation classes and a full classification of cluster tilted algebras of type ilde{A}_n up to derived equivalence, based on combinatorial parameters.

Findings

Mutation classes of ilde{A}_n quivers are explicitly described.

Cluster tilted algebras of type ilde{A}_n are classified up to derived equivalence.

The derived category depends on four combinatorial parameters.

Abstract

We give an explicit description of the mutation classes of quivers of type \tilde{A}_n. Furthermore, we provide a complete classification of cluster tilted algebras of type \tilde{A}_n up to derived equivalence. We show that the bounded derived category of such an algebra depends on four combinatorial parameters of the corresponding quiver.