On the topology of the dual space of crossed product $C^*$-algebras with finite groups
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 391-397
Published online March 13, 2017
Printed March 31, 2017
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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