The Milnor-Moore theorem for L∞ algebras in rational homotopy theory

Abstract

We give a construction of the universal enveloping A∞ algebra of a given L∞ algebra, alternative to the already existing versions. As applications, we derive a higher homotopy algebras version of the classical Milnor-Moore theorem. This proposes a new A∞ model for simply connected rational homotopy types, and uncovers a relationship between the higher order rational Whitehead products in homotopy groups and the Pontryagin-Massey products in the rational loop space homology algebraOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. charged to the Universidad de Málaga/CBU