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The action of a semisimple Lie group on its maximal compact subgroup

Author(s): T. Budak; N. Isik; P. Milnes; J. Pym
Journal: Proc. Amer. Math. Soc. 129 (2001), 1525-1534.
MSC (2000): Primary 54H15, 54H20, 57S20
Posted: January 8, 2001
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Abstract:

In this paper we determine the structure of the minimal ideal in the enveloping semigroup for the natural action of a connected semisimple Lie group on its maximal compact subgroup. In particular, if $G= KAN$ is an Iwasawa decomposition of the group $G$, then the group in the minimal left ideal is isomorphic both algebraically and topologically with the normalizer $M$ of $AN$ in $K.$ Complete descriptions are given for the enveloping semigroups in the cases $G=\text{\rm {SL}}(2, \mathbb{C} )$and $G=\text{\rm {SL}}(2, \mathbb{R} ).$

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Additional Information:

T. Budak
Affiliation: Department of Mathematics, Bogaz\.iç\.i Ün\.ivers\.ites\.i, 80815 Bebek, Istanbul, Turkey
Email: budakt@boun.edu.tr

N. Isik
Affiliation: Department of Mathematics, Bogaz\.iç\.i Ün\.ivers\.ites\.i, 80815 Bebek, Istanbul, Turkey
Email: isikn@boun.edu.tr

P. Milnes
Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
Email: milnes@uwo.ca

J. Pym
Affiliation: Department of Pure Mathematics, University of Sheffield, S3 7RH, England
Email: j.pym@shef.ac.uk

DOI: 10.1090/S0002-9939-01-05984-6
PII: S 0002-9939(01)05984-6
Received by editor(s): July 15, 1999
Posted: January 8, 2001
Additional Notes: The first and second authors were supported by a research grant from Bogaz\.iç\.i University
The third author was supported by NSERC grant A7857
Communicated by: Michael Handel
Copyright of article: Copyright 2001, American Mathematical Society

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