## Abstract

We introduce a type of zero-dimensional dynamical system (a pair consisting of a totally disconnected compact metrizable space along with a homeomorphism of that space), which we call "fiberwise essentially minimal", that is a class that includes essentially minimal systems and systems in which every orbit is minimal. We prove that the associated crossed product C∗-algebra of such a system is an A-algebra. Under the additional assumption that the system has no periodic points, we prove that the associated crossed product C∗-algebra has real rank zero, which tells us that such C∗-algebras are classifiable by K-theory. The associated crossed product C∗-algebras to these nontrivial examples are of particular interest because they are non-simple (unlike in the minimal case).

Original language | English |
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Article number | 2250035 |

Journal | International Journal of Mathematics |

Volume | 33 |

Issue number | 5 |

DOIs | |

State | Published - 1 Apr 2022 |

## Keywords

- C ∗ -algebras
- classification
- dynamical systems
- K -theory
- noncommutative dynamics
- zero-dimensional

## ASJC Scopus subject areas

- Mathematics (all)