The ideal structure of reduced crossed products

TL;DR

This paper studies the ideal structure of reduced crossed product C*-algebras for discrete group actions, establishing conditions for ideal separation and extending key concepts like topological freeness and the Rokhlin property.

Contribution

It provides new sufficient and necessary conditions for ideal separation in reduced crossed products, generalizes the Rokhlin property, and emphasizes the role of exactness in these structures.

Findings

A separates the ideals in A ×_r G under certain conditions

Extension of topological freeness and Rokhlin property concepts

Exactness is crucial for ideal structure analysis

Abstract

Let (A,G) be a C*-dynamical system with G discrete. In this paper we investigate the ideal structure of the reduced crossed product C*-algebra and in particular we determine sufficient - and in some cases also necessary - conditions for A to separate the ideals in Ax_rG. When A separates the ideals in Ax_rG, then there is a one-to-one correspondence between the ideals in Ax_rG and the invariant ideals in A. We extend the concept of topological freeness and present a generalization of the Rokhlin property. Exactness properties of (A,G) turns out to be crucial in these investigations.