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.
Firuz Kamalov
Canadian University of Dubai
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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