The BV formalism for L${}_{\infty }$-algebras

Abstract

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.

20 pages; a version, containing minor changes, to be published in Journal of Homotopy and Related Structures

References in corpus (1)

• Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

Cited by in corpus (4)

• Shifted derived Poisson manifolds associated with Lie pairs
• On a Batalin--Vilkovisky operator generating higher Koszul brackets on differential forms
• Atiyah classes of strongly homotopy Lie pairs
• Quantization of (-1)-Shifted Derived Poisson Manifolds