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

 

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


Author: Takahiro Sudo
Journal: Proc. Amer. Math. Soc. 125 (1997), 3647-3654
MSC (1991): Primary 46L05, 22D25
MathSciNet review: 1415371
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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.


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Additional Information

Takahiro Sudo
Email: sudoh@math.metro-u.ac.jp

DOI: http://dx.doi.org/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
Article copyright: © Copyright 1997 American Mathematical Society