Lie algebras of finite subalgebra rank
type: Item
instance of: scholarly article
title: Lie algebras of finite subalgebra rank
zbMATH Open document ID: 0907.17003
author: Martin J. Evans
author: David Riley
published in: Archiv der Mathematik
publication date: 1999-03-04T00:00:00Z
review text: For \(L\) a Lie algebra over a field \(F\), if \(d(H)\) denotes the minimal number of generators required to generate a subalgebra \(H\) of \(L\), then the subalgebra rank \(r\) of \(L\) is defined to be \(\sup \{d(H) | H\leq L\) and \(d(H)< \infty\}\), and \(L\) is said to be of finite rank if \(r<\infty\). The authors prove that if \(F\) has characteristic 0 or is algebraically closed with characteristic \(p\geq 5\), then every residually finite-dimensional Lie algebra of finite rank \(r\) has finite dimension bounded by an explicit function depending only on \(r\). Separate proofs are provided for the characteristic-zero and positive-characteristic cases.
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 1145741
zbMATH Keywords: subalgebra rank
zbMATH Keywords: residually finite-dimensional Lie algebra of finite rank
MaRDI profile type: Publication
full work available at URL: s000130050108
OpenAlex ID: W1987581157
DOI: 10.1007/S000130050108
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description: scientific article; zbMATH DE number 1145741