Hochschild cohomology of a smash product in the nonsemisimple case

TL;DR

This paper investigates the Hochschild cohomology of smash products of algebras with finite groups, focusing on cases where the group is an extension of a cyclic p-group by a p'-group in characteristic p.

Contribution

It provides new insights into the Hochschild cohomology of smash products in the nonsemisimple case, especially for specific group extensions.

Findings

Established relations between Hochschild cohomology of algebras and their smash products.

Analyzed the case where the group is an extension of a cyclic p-group by a p'-group.

Focused on nonsemisimple algebra cases in characteristic p.

Abstract

In this paper we explore the relations between the Hochschild cohomology of an algebra over some field and the Hochschild cohomology of its smash product with a finite group. Basically we are concentrated on the case where the group under consideration is an extension of a cyclic $p$-group by some $p'$-group, where $p$ is the characteristic of the ground field.