Bounds on the order of generation of SO(n,R) by one-parameter subgroups
type: Item
instance of: scholarly article
title: Bounds on the order of generation of SO(n,R) by one-parameter subgroups
zbMATH Open document ID: 0728.22009
published in: Rocky Mountain Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let G be a compact Lie group and \(X_ 1,...,X_ k\) a set of generators of its Lie algebra \({\mathfrak g}\). Then any element of G can be written as a finite product of exponentials exp \(t_ jX_ j\), \(j\in \{1,...,k\}\). The author addresses the question how many factors of this kind one needs. For \(G=SO(n)\) he constructs various sets of generators via a successive use of the Cartan decomposition of G when viewed as the group of isometries of a compact Riemannian symmetric space. Then he gives uniform bounds for the number of factors needed. In the case SO(3) he shows that any two elements of \({\mathfrak g}\) which are not collinear can be used as generators and calculates the minimal number of factors in terms of the angle between the two infinitesimal rotations (i.e. their axes).
reviewed by: Joachim Hilgert
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 22E60
zbMATH DE Number: 4202612
zbMATH Keywords: compact Lie group
zbMATH Keywords: generators
zbMATH Keywords: Lie algebra
zbMATH Keywords: Cartan decomposition
zbMATH Keywords: group of isometries
zbMATH Keywords: compact Riemannian symmetric space
author: Fátima Silva Leite
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072975
OpenAlex ID: W2060967429
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DOI: 10.1216/RMJM/1181072975
description: scientific article; zbMATH DE number 4202612