BV-operators and secondary Hochschild complex

TL;DR

This paper introduces BV-operators on homotopy G-algebras and applies this to define a BV-operator on the secondary Hochschild cohomology complex of symmetric algebras, linking Gerstenhaber brackets with BV-formalism.

Contribution

It defines BV-operators on homotopy G-algebras and constructs a BV-operator on the secondary Hochschild cohomology complex of symmetric algebras.

Findings

BV-operators determine Gerstenhaber brackets in homotopy G-algebras.

Constructed a BV-operator on the secondary Hochschild cohomology complex.

Links BV-formalism with secondary Hochschild cohomology.

Abstract

We introduce the notion of a BV-operator $\Delta=\{\Delta^n:V^n\longrightarrow V^{n-1}\}_{n\geq 0}$ on a homotopy $G$-algebra $V^\bullet$ such that the Gerstenhaber bracket on $H(V^\bullet)$ is determined by $\Delta$ in a manner similar to the BV-formalism. As an application, we produce a BV-operator on the cochain complex defining the secondary Hochschild cohomology of a symmetric algebra $A$ over a commutative algebra $B$.