Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(2): 391-397

Online first article March 13, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b150688

Copyright © The Korean Mathematical Society.

On the topology of the dual space of crossed product $C^*$-algebras with finite groups

Firuz Kamalov

Canadian University of Dubai

Abstract

In this note we extend our previous result about the structure of the dual of a crossed product $C^*$-algebra $\cp$, when $G$ is a finite group. We consider the space $\widetilde{\Gamma}$ which consists of pairs of irreducible representations of $A$ and irreducible projective representations of subgroups of $G$. Our goal is to endow $\widetilde{\Gamma}$ with a topology so that the orbit space $G\backslash \widetilde{\Gamma}$ is homeomorphic to the dual of $\cp$. In particular, we will show that if $\widehat{A}$ is Hausdorff then $G\backslash\widetilde{\Gamma}$ is homeomorphic to $\widehat{\cp}$.

Keywords: crossed product $C^*$-algebra

MSC numbers: 46L55, 46L05

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