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.
Bibliographical noteFunding Information:
This work was supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, the Institute for Mathematics and its Applications with funds provided by the National Science Foundation, and a Grant from the Simons Foundation (#282349 to A.V.).
© 2016, Tbilisi Centre for Mathematical Sciences.
- Derived brackets
- Homotopical algebra
- Master equation