A universal enveloping for L-infinity algebras

2007/06/11 by Vladimir Baranovsky, Baranovsky, Vladimir
Mathematics · #17B35 #18D50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0706.1396

openalex publication_date 2007/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any L-infinity algebra L, we construct an A-infinity structure on the space of symmetric tensors Sym*(L), which generalizes the classical universal enveloping for Lie algebras. Our construction is based on an invariant homotopy on a cobar construction of the symmetric coalgebra, which is obtained through its relation with permutahedra and Young tableaux.

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