Journal of Operator Theory

Volume 45, Issue 2, Spring 2001 pp. 251-264.

K-theory of simple

$C^*$ -algebras associated with free products of cyclic groups

Authors: Wojciech Szymanski (1), and Shuang Zhang (2)
Author institution: (1) Department of Mathematics, The University of Newcastle, Newcastle, NSW 2308, Australia
(2) Department of Mathematical S ciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, USA

Summary: Let

$\Gamma_\Lambda\leq\Gamma$ be free products of countably many cyclic groups and let

$C(X_\Lambda)\times\Gamma$ denote the crossed product related to an action of

$\Gamma$ on a compact space

$X_\Lambda$ constructed from the homogeneous space

$\Gamma/\Gamma_\Lambda$ and the boundary

$\partial \Gamma$ . Assuming that either

$\Gamma$ is free or

$\Gamma_\Lambda$ is finite we determine the {\rm K}-groups of the crossed products. Among the algebras considered there are both extensions of some Cuntz-Krieger algebras by the compacts and some purely infinite simple

$C^*$ -algebras (nuclear or not).

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