The BV formalism for homotopy Lie algebras

Abstract

The present work concerns certain aspects of homotopy Lie and homotopy Batalin-Vilkovisky structures. In the first part we characterize a class of homotopy BV-algebras canonically associated to strongly homotopy Lie algebras and show that a category of strongly homotopy Lie algebras embeds into a certain subcategory of particularly simple homotopy Batalin-Vilkovisky algebras. In the second part of the work we introduce the notions of coboundary and triangular homotopy Lie bialgebras and discuss a possible a framework for quantization of such bialgebras.