Minimal index of a $C^{*}$-crossed product by a finite group
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- by Ja A Jeong and Gie Hyun Park PDF
- Proc. Amer. Math. Soc. 129 (2001), 2031-2038 Request permission
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 $A$.References
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Additional Information
- Ja A Jeong
- Affiliation: Division of Liberal Arts, Myongji University, Yongin, 449โ728, Korea
- Address at time of publication: BK21 Mathematical Sciences Division, Seoul National University, Seoul, 151-742 Korea
- Email: jajeong@math.snu.ac.kr
- Gie Hyun Park
- Affiliation: Department of Mathematics, Hanshin University, Osan, 447โ791, Korea
- Email: ghpark@hucc.hanshin.ac.kr
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2031-2038
- MSC (2000): Primary 46L05, 46L55
- DOI: https://doi.org/10.1090/S0002-9939-00-05810-X
- MathSciNet review: 1825914