On Hochschild cohomology of a self-injective special biserial algebra obtained by a circular quiver with double arrows

Abstract: We calculate the dimensions of the Hochschild cohomology groups of a self-injective special biserial algebra $\Lambda_{s}$ obtained by a circular quiver with double arrows. Moreover, we give a presentation of the Hochschild cohomology ring modulo nilpotence of $\Lambda_{s}$ by generators and relations. This result shows that the Hochschild cohomology ring modulo nilpotence of $\Lambda_{s}$ is finitely generated as an algebra.