Alexander Voronov

The BV formalism for L_infty-algebras and quantum infty-groups

We interpret the theory of L_infty-algebras using the BV formalism. We introduce r_infty matrices, which are solutions to the Maurer-Cartan equation in the exterior algebra of a dg Lie algebra or, more generally, an L_infty algebra. This equation generalizes the classical Yang-Baxter equation [r,r] = 0 in the exterior algebra of a Lie algebra. We show have such r_infty matrices give rise to triangular L_infty bialgebras and quantum infty-groups. This is a joint work with my graduate student Denis Bashkirov.