The BV formalism for $$L_\infty $$-algebras

• DOI: 10.1007/s40062-016-0129-z
• Publication Date: 2016-04-14T09:38:36Z
• Authors: Denis Bashkirov; Alexander A. Voronov
• Keywords: Morphism; Formalism (music)

Functorial properties of the correspondence between commutative BV$_\infty$-algebras and L$_\infty$-algebras are investigated. The category of L$_\infty$-algebras with L$_\infty$-morphisms is characterized as a certain category of pure BV$_\infty$-algebras with pure BV$_\infty$-morphisms. The functor assigning to a commutative BV$_\infty$-algebra the L$_\infty$-algebra given by higher derived brackets is also shown to have a left adjoint. Cieliebak-Fukaya-Latschev's machinery of IBL$_\infty$- and BV$_\infty$-morphisms is further developed with introducing the logarithm of a map.<br/>20 pages; a version, containing minor changes, to be published in Journal of Homotopy and Related Structures<br/>