Upper bound for the dimension of the center of a solvable Lie algebra
type: Item
instance of: scholarly article
title: Upper bound for the dimension of the center of a solvable Lie algebra
zbMATH Open document ID: 1010.17004
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: According to the Levi decomposition theorem, every solvable Lie algebra \(L\) over a field \(K\) of characteristic zero is a semi-direct sum of its radical \(\text{Rad}(L)=R\) and \(S\cong L/R\), where \(S\) is semisimple. \(S\) has no center and consequently \(Z(L)\subset R\). Thus the study of \(Z(L)\) is reduced to the case \(S=0\), i.e. to the case of solvable Lie algebras. It is shown that the dimension of \(Z(L)\) of finite \(n\)-dimensional solvable Lie algebra having a nilradical of dimension \(r\) admits \(2r-n\) as least upper bound.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 1899928
zbMATH Keywords: solvable Lie algebra
zbMATH Keywords: radical
zbMATH Keywords: center
zbMATH Keywords: dimension
author: J. C. Ndogmo
MaRDI profile type: Publication
full work available at URL: s000120050148
OpenAlex ID: W2043638961
Wikidata QID: Q115390158
DOI: 10.1007/S000120050148
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description: scientific article; zbMATH DE number 1899928