Abstract

Given a Hamiltonian symmetry on a Poisson manifold one can construct a Poisson structure on a reduced manifold. This can be achieved with the Poisson version of the Marsden-Weinstein reduction or equivalently with the BRST-method. Fixing a Lie group action on a manifold, one can define a curved Lie algebra whose Maurer-Cartan elements are Poisson structures together with momentum maps. Poisson structures on the reduced manifold are Maurer-Cartan elements of the usual DGLA of polyvector fields. Thus, reduction is just a map between these two sets of Maurer-Cartan elements. In my talk I want to show that this map is actually the map on Maurer-Cartan elements induced by an $L_infty$-morphism.