The BV Algebra on Hochschild Cohomology Induced by Infinity Inner Products

TL;DR

This paper constructs a BV-structure on Hochschild cohomology for associative and A-infinity algebras with symmetric, non-degenerate inner products, linking it to Gerstenhaber's algebra and extending to homotopy cases.

Contribution

It introduces a BV-structure on Hochschild cohomology for both associative and A-infinity algebras with infinity-inner products, extending known algebraic structures.

Findings

Defined BV-structure on Hochschild cohomology of associative algebras

Extended the BV-structure to A-infinity algebras with infinity-inner products

Connected the structure to Gerstenhaber's original Hochschild cohomology algebra

Abstract

We define a BV-structure on the Hochschild-cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber's original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital A-infinity-algebra with a symmetric and non-degenerate infinity-inner product.