Invariance of the Gerstenhaber algebra structure on Tate-Hochschild cohomology

TL;DR

This paper demonstrates that the Gerstenhaber algebra structure on Tate-Hochschild cohomology remains invariant under certain derived equivalences, extending Keller's earlier results to a broader cohomological context.

Contribution

It adapts Keller's approach to show invariance of the Gerstenhaber algebra on Tate-Hochschild cohomology under singular equivalences of Morita type with level.

Findings

Gerstenhaber algebra structure is preserved under singular equivalences of Morita type with level

Extension of invariance results from Hochschild to Tate-Hochschild cohomology

Provides a new perspective on invariance in derived categories

Abstract

Keller proved in 1999 that the Gerstenhaber algebra structure on the Hochschild cohomology of an algebra is an invariant of the derived category. In this paper, we adapt his approach to show that the Gerstenhaber algebra structure on the Tate-Hochschild cohomology of an algebra is preserved under singular equivalences of Morita type with level, a notion introduced by the author in previous work.