Locally semisimple and maximal subalgebras of the finitary Lie algebras gl(∞), sl(∞), so(∞), and sp(∞)

2008/09/15 by Ivan Dimitrov, Dimitrov, Ivan, Ivan Penkov +1
Mathematics · #17B05 #17B65 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0809.2536

openalex publication_date 2008/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe all locally semisimple subalgebras and all maximal subalgebras of the finitary Lie algebras \gl(∞), \sl(∞), \so(∞), and \sp(∞). For simple finite--dimensional Lie algebras these classes of subalgebras have been described in the classical works of A. Malcev and E. Dynkin. Key words (2000 MSC): 17B05 and 17B65.

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