Tate duality and transfer in Hochschild cohomology

TL;DR

This paper demonstrates that in symmetric algebras, dualising transfer maps in Hochschild cohomology commute with Tate duality, extending a classical result from group cohomology to a broader algebraic context.

Contribution

It generalizes the compatibility of transfer maps and Tate duality from group cohomology to Hochschild cohomology of symmetric algebras.

Findings

Transfer maps in Hochschild cohomology commute with Tate duality.

Extension of a known group cohomology result to symmetric algebras.

Provides a new perspective on duality and transfer in algebraic cohomology.

Abstract

We show that dualising transfer maps in Hochschild cohomology of symmetric algebras commutes with Tate duality. This extends a well-known result in group cohomology.