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

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 ${\mathrm{HH}}^{\ast }(\Lambda )$ 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.

9 pages. arXiv admin note: text overlap with arXiv:1507.07484, arXiv:1201.4182, arXiv:1506.08874; text overlap with arXiv:1512.00738, arXiv:1209.2146 by other authors