The Milnor-Moore theorem for L_\∞ algebras in rational homotopy\n theory

2019/04/29 by José M. Moreno-Fernández, Moreno-Fernández, José Manuel
Mathematics · #16E45 #16S30 #17B55 #18G55 #55P62 #55Q15 #55S30 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1904.12530

openalex publication_date 2019/04/29 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We give a construction of the universal enveloping A_\∞ algebra of a\ngiven L_\∞ algebra, alternative to the already existing versions. As\napplications, we derive a higher homotopy algebras version of the classical\nMilnor-Moore theorem, proposing a new A_\∞ model for simply connected\nrational homotopy types, and uncovering a relationship between the higher order\nrational Whitehead products in homotopy groups and the Pontryagin-Massey\nproducts in the rational loop space homology algebra.\n

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