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arXiv · 2009.12365

The structure of crossed products by automorphisms of $C (X, D)$

Dawn Archey·Julian Buck·N. Christopher Phillips
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Abstract

We construct centrally large subalgebras in crossed products of $C (X, D)$ by automorphisms in which $D$ is simple, $X$ is compact metrizable, the automorphism induces a minimal homeomorphism of $X$, and a mild technical assumption holds. We use this construction to prove structural properties of the crossed product, such as (tracial) $Z$-stability, stable rank one, real rank zero, and pure infiniteness, in a number of examples. Our examples are not accessible via methods based on finite Rokhlin dimension, either because $D$ is not $Z$-stable or because $X$ is infinite dimensional.

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Dawn Archey, Julian Buck, N. Christopher Phillips. 2020-09-25. The structure of crossed products by automorphisms of $C (X, D)$. https://arxiv.org/abs/2009.12365

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