Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras

2010/01/06 by Loïc Foissy, Foissy, Loïc
Mathematics · #16S30 #17B20 #17D25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:16S30 #msc:17B20 #msc:17D25

paper · pdf · doi:10.48550/arxiv.1001.0851

27 pages

arxiv created 2010/01/06 · openalex publication_date 2010/01/06 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize prelie algebras in words of left ideals of the enveloping algebras and in words of modules, and use this result to prove that a simple complex finite-dimensional Lie algebra is not prelie, with the possible exception of f4.

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