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THE DUAL STRUCTURE OF CROSSED PRODUCT ${C}^{\ast } $-ALGEBRAS WITH FINITE GROUPS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  18 January 2013

FIRUZ KAMALOV
FIRUZ KAMALOV*
Affiliation:
Mathematics Department, Canadian University of Dubai, Dubai, UAE email firuz@cud.ac.ae
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Abstract

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We study the space of irreducible representations of a crossed product ${C}^{\ast } $-algebra ${\mathop{A\rtimes }\nolimits}_{\sigma } G$, where $G$ is a finite group. We construct a space $\widetilde {\Gamma } $ which consists of pairs of irreducible representations of $A$ and irreducible projective representations of subgroups of $G$. We show that there is a natural action of $G$ on $\widetilde {\Gamma } $ and that the orbit space $G\setminus \widetilde {\Gamma } $ corresponds bijectively to the dual of ${\mathop{A\rtimes }\nolimits}_{\sigma } G$.

Keywords

irreducible representationscrossed product C∗-algebrafinite groupsdual structure

MSC classification

Secondary: 46L55: Noncommutative dynamical systems 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 243 - 249
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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