Complex finitary simple Lie algebras
type: Item
instance of: scholarly article
title: Complex finitary simple Lie algebras
zbMATH Open document ID: 0932.17022
author: A. A. Baranov
published in: Archiv der Mathematik
publication date: 2000-03-12T00:00:00Z
review text: Let \(K\) be algebraically closed field of characteristic zero, \(V\) be a vector space over \(K\) and \({\mathfrak {gl}}(V)\) be the Lie algebra of linear transformations of \(V\). \(f\in {\mathfrak{gl}}(V)\) is called finitary if \(\dim fV<\infty\). Finitary transformations form an ideal of \({\mathfrak{gl}}(V)\) and any subalgebra of this ideal is called finitary. The author classifies finitary simple Lie algebras over \(K\) and concludes that any such algebra is isomorphic to a special transvection algebra, a finitary orthogonal algebra or a finitary symplectic algebra.
Mathematics Subject Classification ID: 17B65
zbMATH DE Number: 1295480
zbMATH Keywords: finitary simple Lie algebras
zbMATH Keywords: special transvection algebra
zbMATH Keywords: finitary orthogonal algebra
zbMATH Keywords: finitary symplectic algebra
reviewed by: Melih Boral
MaRDI profile type: Publication
full work available at URL: s000130050310
OpenAlex ID: W1988340593
DOI: 10.1007/S000130050310
description: scientific article; zbMATH DE number 1295480