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Operator $K$-Theory for groups which act on Hilbert space
Nigel Higson and Gennadi Kasparov
Abstract.
Let $G$ be a countable discrete group which acts isometrically
and metrically properly on an infinite-dimensional Euclidean space.
We calculate the
$K$-theory groups of the $C^{*}$-algebras $C^{*}_{\max }(G)$ and $C^{*}_{
\smash{\text{red}}}(G)$. Our
result is in accordance with the Baum-Connes conjecture.
Copyright 1997 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 03 (1997), pp. 131-142
- Publisher Identifier: S 1079-6762(97)00037-1
- 1991 Mathematics Subject Classification. Primary 46L20
- Key words and phrases. Baum-Connes conjecture, $C^{*}$-algebras,
$K$-theory
- Received by the editors October 25, 1997
- Posted on December 19, 1997
- Communicated by Masamichi Takesaki
- Comments (When Available)
Nigel Higson
Department of Mathematics, Pennsylvania State University,
University Park, PA 16802
E-mail address: higson@math.psu.edu
Gennadi Kasparov
Institut de Mathématiques de Luminy, CNRS-Luminy-Case 930, 163 Avenue
de Luminy 13288, Marseille Cedex 9, France
E-mail address: kasparov@iml.univ-mrs.fr
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