Structure of crossed products by strictly proper actions on continuous-trace algebras

TL;DR

This paper investigates the ideal structure of crossed product C*-algebras formed from continuous-trace algebras under proper group actions, providing a detailed spectral topology description for specific cases.

Contribution

It offers a concrete description of the spectrum topology of crossed products by proper actions on continuous-trace algebras, especially for discrete and Lie group actions.

Findings

Explicit spectral topology description for crossed products

Analysis for discrete groups and Lie groups

Enhanced understanding of ideal structures in these contexts

Abstract

We examine the ideal structure of crossed products B\rtimes G where B is a continuous-trace C*-algebra and the induced action of G on the spectrum of B is proper. In particular, we are able to obtain a concrete description of the topology on the spectrum of the crossed product in the cases where either G is discrete or G is a Lie group acting smoothly on the spectrum of B.