Structure Theory for One Class of Locally Finite Lie Algebras

2003/10/14 by L. A. Simonian, Simonian, L. A.
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.math/0310208

arxiv created 2003/10/14 · openalex publication_date 2003/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements x₁, x₂,..., x_k of such an algebra L there is finite-dimensional subalgebra A which contains these elements and L(adA)ⁿ⊂ A for some integer n. For such algebras I prove several structure theorems that can be regarded as generalizations of the classical structure theorems of the finite-dimensional Lie algebras theory.

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