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

Abstract

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