Crossed product C*-algebras associated with non-minimal actions on the circle

TL;DR

This paper studies crossed product C*-algebras from non-minimal free actions of abelian groups on the circle, revealing their structure, nuclear properties, and K-theory, extending previous work in the field.

Contribution

It extends the analysis of crossed product C*-algebras for non-minimal actions, providing new classifications and computations of their K-theory and ideal structure.

Findings

Constructed a large class of unital separable nuclear non-simple C*-algebras.

Established an improved uniform upper bound for nuclear dimension.

Computed ordered K-theory and trace pairing for G = Z^d.

Abstract

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable nuclear and non-simple C*-algebras that are quasidiagonal, have stable rank one, and admit a unique tracial state. We determine their ideal structure and establish an improved uniform upper bound for their nuclear dimension. Finally, in the case $G = \mathbb{Z}^d$, we compute the ordered K-theory and its trace pairing.