Tate-Hochschild Cohomology of Radical Square Zero Algebras

TL;DR

This paper provides a combinatorial approach to computing the Tate-Hochschild cohomology of radical square zero algebras and explores their Gerstenhaber algebra structures for specific classes.

Contribution

It introduces a novel combinatorial method for describing Tate-Hochschild cohomology and computes its algebraic structure for certain radical square zero algebras.

Findings

Combinatorial description of Tate-Hochschild cohomology for radical square zero algebras

Explicit computation of Gerstenhaber algebra structures in specific cases

New insights into the algebraic structure of these cohomologies

Abstract

For algebras with radical square zero, we give a combinatorial description to the Tate-Hochschild cohomology. We compute the Gerstenhaber algebra structure on the Tate-Hochschild cohomology for some classes of such algebras.