Abstract

Let G be a simply connected Lie group. We denote by C(G) the differential graded Hopf algebra of smooth singular chains on G. We will explain how the category of modules over C(G) can be described infinitesimally in terms of representations of the differential graded Lie algebra Tg, which is universal for the Cartan relations. In case G is compact, this correspondence can be promoted to an A-infinity equivalence of differential graded categories. We will also explain how this equivalence is related to Chern-Weil theory and higher local systems on classifying spaces. This talk is based on joint work with Alexander Quintero Vélez.