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

P. A.U.L. Herstedt

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that crossed products of fiberwise essentially minimal zero-dimensional dynamical systems, a class that includes systems in which all orbit closures are minimal, 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 associated crossed product C∗ -algebras as well. We additionally explore the K-theory of such crossed products and the Bratteli diagrams associated to the dynamical systems.

Original languageEnglish
JournalErgodic Theory and Dynamical Systems
DOIs
StateAccepted/In press - 1 Jan 2023

Keywords

  • Bratteli diagrams
  • C-algebras
  • K-theory
  • dynamical systems

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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