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Operator $K$-theory for groups which act properly and isometrically on Hilbert space


Authors: Nigel Higson and Gennadi Kasparov
Journal: Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 131-142
MSC (1991): Primary 46L20
Published electronically: December 19, 1997
MathSciNet review: 1487204
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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.


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Additional Information

Nigel Higson
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, PA 16802
Email: higson@math.psu.edu

Gennadi Kasparov
Affiliation: Institut de Mathématiques de Luminy, CNRS-Luminy-Case 930, 163 Avenue de Luminy 13288, Marseille Cedex 9, France
Email: kasparov@iml.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S1079-6762-97-00038-3
Keywords: Baum-Connes conjecture, $C^{*}$-algebras, $K$-theory
Received by editor(s): October 25, 1997
Published electronically: December 19, 1997
Additional Notes: The first author was partially supported by an NSF grant.
Communicated by: Masamichi Takesaki
Article copyright: © Copyright 1997 American Mathematical Society