Hochschild cohomology of fully group-graded algebras as Mackey functor

TL;DR

This paper demonstrates that Hochschild cohomology for a specific class of fully group-graded algebras can be structured as a Mackey functor, utilizing transfer maps between symmetric algebra cohomologies.

Contribution

It establishes a new connection between Hochschild cohomology and Mackey functors for fully group-graded algebras, expanding the theoretical framework.

Findings

Hochschild cohomology forms a Mackey functor for these algebras

Transfer maps are used to relate cohomologies of symmetric algebras

Provides a new perspective on algebraic structures via Mackey functors

Abstract

We prove that Hochschild cohomology of a certain class of fully group-graded algebras is a Mackey functor. We use the machinery of transfer maps between the Hochschild cohomology of symmetric algebras.