The nuclear dimension of C*-algebras associated to homeomorphisms

TL;DR

This paper proves that crossed product C*-algebras formed from automorphisms of finite-dimensional locally compact spaces have finite nuclear dimension, extending previous results to non-free automorphisms and applying to certain non-nilpotent groups.

Contribution

It generalizes the finite nuclear dimension result to all automorphisms on finite-dimensional spaces, including non-free cases, and applies to specific non-nilpotent group C*-algebras.

Findings

Crossed products of C_0(X) by any automorphism have finite nuclear dimension.

Extension of finite nuclear dimension results to non-free automorphisms.

Group C*-algebras of certain non-nilpotent groups have finite nuclear dimension.

Abstract

We show that if X is a finite dimensional locally compact Hausdorff space, then the crossed product of C_0(X) by any automorphism has finite nuclear dimension. This generalizes previous results, in which the automorphism was required to be free. As an application, we show that group C*-algebras of certain non-nilpotent groups have finite nuclear dimension.