Hochschild cohomology of socle deformations of a class of Koszul self-injective algebras

TL;DR

This paper investigates the Hochschild cohomology of socle deformations of certain Koszul self-injective algebras, revealing that their cohomology ring modulo nilpotence is finitely generated with Krull dimension 2.

Contribution

It provides a detailed analysis of Hochschild cohomology for socle deformations of a specific class of Koszul self-injective algebras, linking deformation theory and cohomology.

Findings

Hochschild cohomology ring modulo nilpotence is finitely generated.

The cohomology ring has Krull dimension 2.

Results apply to algebras related to the Drinfeld double of generalized Taft algebras.

Abstract

We consider the socle deformations arising from formal deformations of a class of Koszul self-injective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence is a finitely generated commutative algebra of Krull dimension 2.