Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
type: Item
instance of: scholarly article
title: Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
zbMATH Open document ID: 1022.22021
author: Helge Glöckner
published in: Journal of Functional Analysis
publication date: 2003-03-26T00:00:00Z
review text: The author studies the question whether a given infinite-dimensional Lie group has a complexification. He answers the question completely by giving necessary and sufficient conditions for the so-called Baker-Campbell-Hausdorff (BCH) Lie groups. This class of groups is characterized by the existence of neighborhoods in the Lie algebra on which the exponential function is a diffeomorphism and the multiplication (transported back via the exponential function) is given by the Baker-Campbell-Hausdorff formula. This class of groups includes Banach Lie groups, mapping groups, and direct limit groups but not diffeomorphism groups. In the process the author develops the basic Lie theory for BCH Lie groups as well as the basic properties for various types of mapping groups.
reviewed by: Joachim Hilgert
Mathematics Subject Classification ID: 22E65
zbMATH DE Number: 1888353
zbMATH Keywords: infinite-dimensional Lie group
zbMATH Keywords: complexification
zbMATH Keywords: Baker-Campbell-Hausdorff (BCH) Lie groups
zbMATH Keywords: exponential function
zbMATH Keywords: Baker-Campbell-Hausdorff formula
zbMATH Keywords: Banach Lie groups
zbMATH Keywords: mapping groups
zbMATH Keywords: direct limit groups
MaRDI profile type: Publication
full work available at URL: jfan.2002.3942
OpenAlex ID: W1963863391
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DOI: 10.1006/JFAN.2002.3942
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description: scientific article; zbMATH DE number 1888353