MS Seminar (Mathematics - String Theory)

Speaker: Alexander Voronov (U of Minnesota)
Title: The BV formalism for L_infty-algebras
Date: Fri, Jan 16, 2015, 15:30 - 17:00
Place: Seminar Room B
Abstract: I will discuss BV_infty-morphisms and the category of BV_infty-algebras. The category of L_infty-algebras with L_infty-morphisms will be characterized as a certain subcategory of the category of BV_infty-algebras. This provides a Fourier-dual, BV alternative to the standard characterization of the category of L_infty-algebras as a subcategory of the category of dg cocommutative coalgebras or formal pointed dg manifolds. In particular, the coalgebra codifferential on the symmetric coalgebra S(g[1]) encoding the structure of an L_infty-algebra on a graded vector space g turns into a square-zero differential operator with linear coefficients on the symmetric algebra (g[-1]). This symmetric algebra also presents a left adjoint to the functor assigning to a BV_infty-algebra the L_infty-algebra given by higher derived brackets. The talk is based on a joint work with my student Denis Bashkirov.