The Milnor-Moore theorem for $L_{\infty }$ algebras in rational homotopy theory

Abstract

We give a construction of the universal enveloping $A_{\infty }$ algebra of a given $L_{\infty }$ algebra, alternative to the already existing versions. As applications, we derive a higher homotopy algebras version of the classical Milnor-Moore theorem, proposing a new $A_{\infty }$ model for simply connected rational homotopy types, and uncovering a relationship between the higher order rational Whitehead products in homotopy groups and the Pontryagin-Massey products in the rational loop space homology algebra.

References in corpus (1)

• Homological perturbation theory for algebras over operads