The homotopy Lie algebra of classifying spaces

Abstract

Let X be a 1-connected CW-complex of finite type and L x its rational homotopy Lie algebra. In this work, we show that there is a spectral sequence whose E 2 term is the Lie algebra Ext UL x ( Q, L x ), and which converges to the homotopy Lie algebra of the classifying space B autX. Moreover, some terms of this spectral sequence are related to derivations of L x and to the Gottlieb group of X.