Journal of Operator Theory

Volume 69, Issue 1, Winter 2013 pp. 17-31.

Crossed products by

$\alpha$ -simple automorphisms on

$C^*$ -algebras

$C(X,A)$

Authors: Jiajie Hua
Author institution: Department of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, 314001, P.R. China

Summary: Let

$X$ be a Cantor set, and let

$A$ be a unital separable simple amenable

$C^*$ -algebra with tracial rank zero which satisfies the Universal Coefficient Theorem. We use

$C(X,A)$ to denote the set of all continuous functions from

$X$ to

$A$ ; let

$\alpha$ be an automorphism on

$C(X,A)$ . Suppose that

$C(X,A)$ is

$\alpha$ -simple and

$[\alpha|_{1\otimes A}]=[\mathrm{id}|_{1\otimes A}]$ in

$KL(1\otimes A,C(X, A))$ . We show that

$C(X,A)\\ \rtimes_{\alpha} \mathbb{Z}$ has tracial rank zero.

DOI: http://dx.doi.org/10.7900/jot.2010jun21.1892
Keywords: Crossed products,

$\alpha$ -simple, tracial rank zero

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