The BV formalism for L∞ -algebras

Abstract

Functorial properties of the correspondence between commutative BV ∞-algebras and L∞-algebras are investigated. The category of L∞-algebras with L∞-morphisms is characterized as a certain category of pureBV ∞-algebras with pureBV ∞-morphisms. The functor assigning to a commutative BV ∞-algebra the L∞-algebra given by higher derived brackets is also shown to have a left adjoint. Cieliebak-Fukaya-Latschev’s machinery of IBL ∞- and BV ∞-morphisms is further developed with introducing the logarithm of a map.