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arXiv · 2111.06380

A dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems

Paul Herstedt
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Abstract

We prove that crossed products of fiberwise essentially minimal zero-dimensional dynamical systems have isomorphic $ K $-theory if and only if the dynamical systems are strong orbit equivalent. Under the additional assumption that the dynamical systems have no periodic points, this gives a classification theorem including isomorphism of the $ C^* $-algebras as well. We additionally explore the $ K $-theory of such crossed products and the Bratteli diagrams associated to the dynamical systems.

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Paul Herstedt. 2021-11-11. A dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems. https://doi.org/10.1017/etds.2023.104

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