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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: T. Budak, N. Isik, P. Milnes and J. Pym
Journal: Proc. Amer. Math. Soc. 129 (2001), 1525-1534
MSC (2000): Primary 54H15, 54H20, 57S20
Published electronically: January 8, 2001
MathSciNet review: 1814178
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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, Boğazıçı Ünıversıtesı, 80815 Bebek, İstanbul, Turkey
Email: budakt@boun.edu.tr

N. Isik
Affiliation: Department of Mathematics, Boğazıçı Ünıversıtesı, 80815 Bebek, İstanbul, 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: http://dx.doi.org/10.1090/S0002-9939-01-05984-6
PII: S 0002-9939(01)05984-6
Received by editor(s): July 15, 1999
Published electronically: January 8, 2001
Additional Notes: The first and second authors were supported by a research grant from Boğazıçı\ University
The third author was supported by NSERC grant A7857
Communicated by: Michael Handel
Article copyright: © Copyright 2001 American Mathematical Society