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1 March 2001 The trace on the K-theory of group C*-algebras
Thomas Schick
Duke Math. J. 107(1): 1-14 (1 March 2001). DOI: 10.1215/S0012-7094-01-10711-4

Abstract

The canonical trace on the reduced C*-algebra of a discrete group gives rise to a homomorphism from theK-theory of this C*-algebra to the real numbers. Thi s paper studies the range of this homomorphism. For torsion-free groups, the Baum-Connes conjecture, together with Atiyah's L2-index theorem, implies that the range consists of the integers.

We give a direct and elementary proof that if G acts on a tree and admits a homomorphism α to another group H whose restriction α|Gv to every stabilizer group of a vertex is injective, then

trGG(K(C*r H))⊂trH(K(C*rH)).

This follows from a general relative Fredholm module technique.

Examples are in particular HNN-extensions of H where the stable letter acts by conjugation with an element of H, or amalgamated-free products G=H*UH of two copies of the same groups along a subgroup U.

Citation

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Thomas Schick. "The trace on the K-theory of group C*-algebras." Duke Math. J. 107 (1) 1 - 14, 1 March 2001. https://doi.org/10.1215/S0012-7094-01-10711-4

Information

Published: 1 March 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1020.46023
MathSciNet: MR1815247
Digital Object Identifier: 10.1215/S0012-7094-01-10711-4

Subjects:
Primary: 46L80
Secondary: 19K14, 19K35, 19K56

Rights: Copyright © 2001 Duke University Press

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Vol.107 • No. 1 • 1 March 2001
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