BD algebras and group cohomology

TL;DR

This paper introduces BD algebras, a new algebraic structure similar to BV algebras but with an increasing degree operator, and explores their construction within group cohomology.

Contribution

It defines BD algebras, compares them to BV algebras, and develops methods to construct BD algebras in the context of group cohomology.

Findings

BD algebras are structurally similar to BV algebras.

Methods for constructing BD algebras in group cohomology are established.

The degree +1 operator in BD algebras offers new algebraic insights.

Abstract

BD algebras (Beilinson-Drinfeld algebras) are algebraic structures which are defined similarly to BV algebras (Batalin-Vilkovisky algebras). The equation defining the BD operator has the same structure as the equation for BV algebras, but the BD operator is increasing with degree +1. We obtain methods of constructing BD algebras in the context of group cohomology.