Infinitesimally generated subsemigroups of motion groups
type: Item
instance of: scholarly article
title: Infinitesimally generated subsemigroups of motion groups
zbMATH Open document ID: 0745.22005
published in: Rocky Mountain Journal of Mathematics
publication date: 1992-06-25T00:00:00Z
review text: A Lie wedge \(W\) in the Lie algebra of a Lie group \(G\) is said to be global if there exists a closed subsemigroup \(S\) of \(G\) such that the tangent wedge \(L(S)\) of \(S\) is \(W\). The author investigates globality questions in Lie groups which are motion groups (groups of the form \(KA\) where \(K\) is a compact subgroup and \(A\) is a normal abelian subgroup). He characterizes a special class of Lie wedges called semialgebras in the Lie algebras of motion groups and gives a simple necessary and sufficient condition for globality. This condition is automatically satisfied if \(G\) is simply connected.
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 22E60
zbMATH DE Number: 14138
zbMATH Keywords: Lie group
zbMATH Keywords: tangent wedge
zbMATH Keywords: Lie wedges
zbMATH Keywords: semialgebras
zbMATH Keywords: Lie algebras of motion groups
zbMATH Keywords: globality
author: Joachim Hilgert
reviewed by: Jimmie D. Lawson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072974
OpenAlex ID: W2016392177
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DOI: 10.1216/RMJM/1181072974
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description: scientific article; zbMATH DE number 14138