Homotopy DG algebras induce homotopy BV algebras

TL;DR

This paper demonstrates that the tensor algebra of a differential graded algebra naturally acquires a BV algebra structure, and extends this to BV-infinity algebras for A-infinity algebras, revealing deep algebraic connections.

Contribution

It establishes a new link between homotopy algebra structures and BV algebra frameworks, generalizing to BV-infinity algebras for A-infinity cases.

Findings

Tensor algebra of a dg algebra forms a differential BV algebra.

Tensor algebra of an A-infinity algebra forms a commutative BV-infinity algebra.

Provides a new perspective on homotopy algebra structures and BV formalisms.

Abstract

Let TA denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then TA is a differential Batalin-Vilkovisky algebra. Moreover, if A is an A-infinity algebra, then TA is a commutative BV-infinity algebra.