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

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.

References in corpus (3)

• On triangulated orbit categories
• Generalized cluster complexes and Coxeter combinatorics
• Combinatorial derived invariants for gentle algebras

Cited by in corpus (5)

• Singularity categories of gentle algebras
• Perverse equivalences, BB-tilting, mutations and applications
• Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D
• Derived equivalence classification of the cluster-tilted algebras of Dynkin type E
• The AG-invariant for (m+2)-angulations