The Jordan socle and finitary Lie algebras
type: Item
instance of: scholarly article
title: The Jordan socle and finitary Lie algebras
zbMATH Open document ID: 1104.17019
author: Antonio Fernández López
author: E. Garcia
author: Miguel Gómez Lozano
published in: Journal of Algebra
publication date: 2005-02-22T00:00:00Z
review text: The goal of the paper under review is to study simple finitary Lie algebras and their algebras of derivations by using methods from the theory of Jordan systems. (We refer to the paper, which is clearly written, for the relevant definitions.) In a related paper [Commun. Algebra 32, No. 10, 3807--3824 (2004; Zbl 1088.17010)] the same authors have developed a socle theory for \(3\)-graded Lie algebras via Jordan pairs. In this paper it is shown that this socle is independent of the chosen grading, when the gradings are effective; and a definition of a Jordan socle is given for nondegenerate, but not necessarily \(3\)-graded, Lie algebras. A description of nondegenerate Lie algebras with essential Jordan socle is then obtained. In doing so, the algebras of derivations of simple finitary Lie algebras of infinite dimension over algebraically closed fields of characteristic zero are computed.
reviewed by: Andrea Caranti
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17C50
zbMATH DE Number: 2136740
zbMATH Keywords: Lie algebras
zbMATH Keywords: grading
zbMATH Keywords: finitary algebra
zbMATH Keywords: socle
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.06.013
OpenAlex ID: W2161656586
Wikidata QID: Q115351717
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DOI: 10.1016/J.JALGEBRA.2004.06.013
description: scientific article; zbMATH DE number 2136740