Lie algebras whose proper subalgebras are either semisimple, abelian or almost-abelian
type: Item
instance of: scholarly article
title: Lie algebras whose proper subalgebras are either semisimple, abelian or almost-abelian
zbMATH Open document ID: 0817.17008
author: Vicente R. Varea
published in: Hiroshima Mathematical Journal
publication date: 1995-08-08T00:00:00Z
review text: The author first considers Lie algebras \(L\) having an element \(x\) such that \(C_ L (x)\) is abelian and \(\dim N_ L (C_ L (x))/ C_ L (x)\leq 1\). He also studies the structure of nonsolvable Lie algebras all of whose proper subalgebras are either semisimple, abelian, or almost abelian. He then uses these results in a study of upper semi-modular and relatively complemented Lie algebras. He also obtains information on the structure of Lie algebras which are simple and minimal non-modular, and he determines the Lie algebras with a subalgebra lattice of length 3.
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 681271
zbMATH Keywords: nonsolvable Lie algebras
zbMATH Keywords: upper semi-modular
zbMATH Keywords: relatively complemented
zbMATH Keywords: simple
zbMATH Keywords: minimal non-modular
zbMATH Keywords: subalgebra lattice of length 3
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206128023
OpenAlex ID: W1512939325
DOI: 10.32917/HMJ/1206128023
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description: scientific article; zbMATH DE number 681271