Cyclic brace relation and BV structure on open-closed Hochschild cohomology

TL;DR

This paper establishes a BV algebra structure on the open-closed Hochschild cohomology of cyclic, unital open-closed homotopy algebras, extending the Gerstenhaber structure with cyclic brace operations.

Contribution

It introduces a cochain-level identity with cyclic brace operations to produce a BV algebra structure on the Hochschild cohomology of cyclic, unital OCHAs.

Findings

BV algebra structure on open-closed Hochschild cohomology

Extension of Gerstenhaber algebra to BV algebra in this context

Use of cyclic brace operations to formulate key identities

Abstract

For an open-closed homotopy algebra (OCHA), the previous work indicates that there is an open-closed version of Hochschild cohomology with a canonical Gerstenhaber algebra structure. If this OCHA is further cyclic and unital in the sense of Kajiura and Stasheff, we produce a BV algebra structure on this cohomology via a cochain-level identity formulated with cyclic brace operations.