The surjectivity of the exponential map for certain Lie groups
type: Item
instance of: scholarly article
title: The surjectivity of the exponential map for certain Lie groups
zbMATH Open document ID: 0834.22011
DOI: 10.1007/BF01765631
author: Martin Moskowitz
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-04-01T00:00:00Z
review text: The results of this paper can be viewed as strengthening and generalizing results of \textit{K. H. Hofmann} and \textit{A. Mukherjea} [Math. Ann. 234, 263-273 (1978; Zbl 0382.22005)] and are also related to earlier results of Dixmier and Saito. The author proves the following theorem (Theorem 2.1): The exponential map is surjective for any connected, non compact centerless, rank 1 simple Lie group. -- The group is found by considering such a group as the connected group of isometries of a non compact symmetric space \(G/K\) of negative curvature. The main theorem (Theorem 3.2) then implies, that for a centerless real semisimple Lie group, whose non compact, non rank 1 simple factors have only one conjugacy class of Cartan subgroups, the exponential map is always surjective.
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 22E10
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 22E60
zbMATH DE Number: 711475
zbMATH Keywords: exponential Lie group
zbMATH Keywords: exponential map
zbMATH Keywords: simple Lie group
zbMATH Keywords: non compact symmetric space
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: Cartan subgroups
reviewed by: Günter Czichowski
MaRDI profile type: Publication
Wikidata QID: Q115393194
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full work available at URL: https://doi.org/10.1007/bf01765631
OpenAlex ID: W1973078787
description: scientific article; zbMATH DE number 711475