Cluster tilting modules for mesh algebras

Abstract

We study cluster tilting modules in mesh algebras of Dynkin type as defined in [12], providing a new proof for their existence. Except for type G2, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We further study their mutation, providing an example of mutation in an abelian category which is not stably 2-Calabi-Yau, and explicitly describe the combinatorics.