Lie algebras with few centralizer dimensions.
type: Item
instance of: scholarly article
title: Lie algebras with few centralizer dimensions.
zbMATH Open document ID: 1035.17017
DOI: 10.1016/S0021-8693(02)00558-6
author: Yiftach Barnea
author: I. M. Isaacs
published in: Journal of Algebra
publication date: 2003-04-02T00:00:00Z
review text: Inspired by results in group theory, the authors consider the structure of complex Lie algebras \(L\) which have the property that centralizers of the elements of \(L\) have only two possible dimensions. Nonnilpotent \(L\) have dim\((L/Z(L))\) less than or equal to three and \(L/Z(L)\) is isomorphic to 1. the two dimensional nonabelian Lie algebra or 2. the three dimensional simple Lie algebra or 3. the three dimensional Lie algebra with basis \({a,x,y}\) and multiplication \([a,x]=x, [a,y]=-y\) and \([x,y]=0.\) If \(L\) is nilpotent, then the nilpotency class of \(L\) is at most 3.
reviewed by: Ernest L. Stitzinger
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 1891323
zbMATH Keywords: centralizers
MaRDI profile type: Publication
cites work: Introduction to Lie Algebras and Representation Theory
cites work: On finite \(p\)-groups which have only two conjugacy lengths
cites work: On Finite Groups with Given Conjugate Types I
Wikidata QID: Q115340522
description: scientific article; zbMATH DE number 1891323