Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Stable rank of the reduced $C^{*}$-algebras of non-amenable Lie groups of type I

Author(s): Takahiro Sudo
Journal: Proc. Amer. Math. Soc. 125 (1997), 3647-3654.
MSC (1991): Primary 46L05, 22D25
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: In this paper we show that stable rank of the reduced $C^{*}$-algebras of connected non-compact real semi-simple Lie groups is estimated by real rank of these groups. We extend this result to the case of connected reductive Lie groups and partially even to the case of connected non-amenable real Lie groups of type I. As a corollary, we show that the product formula of stable rank holds for locally compact, $\sigma $-compact non-amenable groups of type I.

References:

[BM]
R. Boyer and R. Martin, The regular group $C^{*}$-algebra for real rank one groups, Proc. Amer. Math. Soc. 59 (1976), 371-376. MR 57:16464

[D]
J. Dixmier, $C^{*}$-Algebras, North-Holland, Amsterdam-New York-Oxford, 1962.

[F]
J. M. G. Fell, Weak containment and Kronecker products of group representations, Pacific J. Math. 13 (1963), 503-510. MR 27:5865

[FD]
J. M. G. Fell and R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, vol. 2, Academic Press, 1988. MR 90c:46002

[HV]
P. de la Harpe et A. Valette, La propriété $(T)$ de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France, 1989. MR 90m:22001

[Ka]
E. Kaniuth, Group $C^{*}$-algebras of real rank zero or one, Proc. Amer. Math. Soc. 119 (1993), 1347-1354. MR 94a:46074

[Kn]
A. W. Knapp, Representation Theory of Semisimple Groups, An Overview Based on Examples, Princeton Univ. Press, Princeton-New Jersey, 1986. MR 87j:22022

[Ko]
B. Kostant, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627-642. MR 39:7031

[L]
R. L. Lipsman, The dual topology for the principal and discrete series on semisimple groups, Trans. Amer. Math. Soc. 152 (1970), 399-417. MR 42:4673

[R]
M. A. Rieffel, Dimension and stable rank in the K-theory of $C^{*}$-algebras, Proc. London Math. Soc. 46 (1983), 301-333. MR 84g:46085

[ST1]
T. Sudo and H. Takai, Stable rank of the $C^{*}$-algebras of nilpotent Lie groups, Internat. J. Math. 6 (1995), 439-446. MR 96b:46083

[ST2]
-, Stable rank of the $C^{*}$-algebras of solvable Lie groups of type I, preprint (1996).

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L05, 22D25

Retrieve articles in all Journals with MSC (1991): 46L05, 22D25

Additional Information:

Takahiro Sudo
Affiliation: Department of Mathematics, Tokyo Metropolitan University, 1-1 Minami Ohsawa, Hachioji-shi, Tokyo 192-03, Japan
Email: sudoh@math.metro-u.ac.jp

DOI: 10.1090/S0002-9939-97-04034-3
PII: S 0002-9939(97)04034-3
Received by editor(s): April 4, 1996
Received by editor(s) in revised form: July 15, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google