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.

References in corpus (3)

• Multiplicative structures for Koszul algebras
• Resolutions over Koszul algebras
• Support varieties and the Hochschild cohomology ring modulo nilpotence