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 | References | Similar Articles | Additional Information

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 is an Iwasawa decomposition of the group , then the group in the minimal left ideal is isomorphic both algebraically and topologically with the normalizer of in Complete descriptions are given for the enveloping semigroups in the cases and

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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

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