Transvections as generators of the special linear group over the quaternions
type: Item
instance of: scholarly article
title: Transvections as generators of the special linear group over the quaternions
zbMATH Open document ID: 0665.20024
DOI: 10.1016/0022-4049(89)90024-8
author: Jerry Malzan
author: Erich W. Ellers
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: Transvections play a prominent role as generators of the special linear group of a finite dimensional vector space over a commutative field. A naturally arising question is to determine the minimal number \(\ell (M)\) of transvections needed to factorize each transformation M in the special linear group into transvections. The authors tackle the corresponding problem for a right vector space over a special skewfield, namely the quaternions. Using normal forms they show \(\ell (M)=\dim (M-1)V\) for a large class of transformations M. For all other transformations it is easy to see that \(\ell (M)=\dim (M-1)V+i\) where \(0\leq i\leq 3\).
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 4087920
zbMATH Keywords: generators
zbMATH Keywords: special linear group
zbMATH Keywords: transvections
zbMATH Keywords: quaternions
reviewed by: Huberta Lausch
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90024-8
OpenAlex ID: W2084923201
cites work: Q3227596
cites work: Products of reflections in the general linear group over a division ring
cites work: Decomposition of equiaffinities into reflections
cites work: Products of reflections in
cites work: Products of Transvections
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description: scientific article; zbMATH DE number 4087920