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arXiv · 1507.07524

A Criterion for $\mathcal{Z}$-Stability with Applications to Crossed Products

Julian Buck
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Abstract

Building on an argument by Toms and Winter, we show that if $A$ is a simple, separable, unital, $\mathcal{Z}$-stable C*-algebra, then the crossed product of $C(X,A)$ by an automorphism is also Z-stable, provided that the automorphism induces a minimal homeomorphism on $X$. As a consequence, we observe that if $A$ is nuclear and purely infinite then the crossed product is a Kirchberg algebra.

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Julian Buck. 2015-07-27. A Criterion for $\mathcal{Z}$-Stability with Applications to Crossed Products. https://arxiv.org/abs/1507.07524

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