The Second Hochschild Cohomology Group for a Class of One-Parametric Self-Injective Algebras

TL;DR

This paper calculates the second Hochschild cohomology group for a specific class of self-injective algebras of tame type, linking it to their deformation theory and extending understanding of their algebraic structure.

Contribution

It provides the first explicit computation of the second Hochschild cohomology for non-weakly symmetric one-parametric self-injective algebras of tame type.

Findings

Determined the second Hochschild cohomology group for the class of algebras.

Connected cohomology results to algebra deformations.

Extended classification results to cohomological properties.

Abstract

In this paper we determine the second Hochschild cohomology group for a class of self-injective algebras of tame representation type namely, those which are standard one-parametric but not weakly symmetric. These were classifed up to derived equivalence by Bocian, Holm and Skowro\'nski. We connect this to the deformation of these algebras.