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Minimal index of a $C^{*}$-crossed product by a finite group

Authors: Ja A Jeong and Gie Hyun Park
Journal: Proc. Amer. Math. Soc. 129 (2001), 2031-2038
MSC (2000): Primary 46L05, 46L55
Published electronically: December 4, 2000
MathSciNet review: 1825914
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Abstract: Let $A\times_{\alpha}G$ be the $C^{*}$-crossed product of a simple unital $C^{*}$-algebra $A$ by a finite group $G$. In this paper we show that the canonical conditional expectation from $A\times_{\alpha}G$ to $A$ has the minimal index if $A\times_{\alpha}G$ is simple. It is also proved that if $\alpha$ is an outer action, then the canonical one is the unique conditional expectation of index-finite type from $A\times_\alpha G$ to $A$, while there are infinitely many conditional expectations when a nontrivial subgroup of $G$ acts innerly on $A$.

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Additional Information

Ja A Jeong
Affiliation: Division of Liberal Arts, Myongji University, Yongin, 449–728, Korea
Address at time of publication: BK21 Mathematical Sciences Division, Seoul National University, Seoul, 151-742 Korea

Gie Hyun Park
Affiliation: Department of Mathematics, Hanshin University, Osan, 447–791, Korea

Received by editor(s): May 3, 1999
Received by editor(s) in revised form: November 10, 1999
Published electronically: December 4, 2000
Additional Notes: The first author was partially supported by GARC-KOSEF and BSRI
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society