Hochschild cohomology of $m$-Cluster tilted algebras of type $\widetilde{\mathbb{A}}$

Abstract

In this paper, we compute the dimension of the Hochschild cohomology groups of any $m$-cluster tilted algebra of type $\tilde{\mathbb{A}}$. Moreover, we give conditions on the bounded quiver of an $m$-cluster tilted algebra $\Lambda$ of type $\tilde{\mathbb{A}}$ such that the Gerstenhaber algebra $\operatorname{HH}^*(\Lambda)$ has non-trivial multiplicative structures. We also show that the derived class of gentle $m$-cluster tilted algebras is not always completely determined by the Hochschild cohomology.