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

Higson, Nigel; Kasparov, Gennadi

doi:10.1090/S1079-6762-97-00038-3

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
DOI: https://doi.org/10.1090/S1079-6762-97-00038-3
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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