The Koszul-Tate type resolution for Gerstenhaber-Batalin-Vilkovisky algebras

Abstract

Tate provided an explicit way to kill a nontrivial homology class of a commutative differential graded algebra over a commutative noetherian ring R in Tate (Ill J Math 1: 14-27, 1957). The goal of this article is to generalize his result to the case of GBV (Gerstenhaber-Batalin-Vilkovisky) algebras and, more generally, the descendant L-infinity-algebras. More precisely, for a given GBV algebra ((A) over tilde = circle plus(m >= 0)A(m), delta, l(2)(delta)), we provide another explicit GBV algebra ((A) over tilde = circle plus(m >= 0) (A) over tilde (m), (delta) over tilde, l(2)((delta) over tilde)) such that its total homology is the same as the degree zero part of the homology H-0(A, delta) of the given GBV algebra (A, delta, l(2)(delta)).