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

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 $C^{\ast }$-algebras as well. We additionally explore the $K$-theory of such crossed products and the Bratteli diagrams associated to the dynamical systems.

20 pages

References in corpus (2)

• The category of ordered Bratteli diagrams
• AT-algebras from fiberwise essentially minimal zero-dimensional dynamical systems