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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Spectra for compact quantum group coactions and crossed products


Authors: Raluca Dumitru and Costel Peligrad
Journal: Trans. Amer. Math. Soc. 364 (2012), 3699-3713
MSC (2010): Primary 47L65, 20G42
Published electronically: March 9, 2012
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Abstract: We present definitions of both the Connes spectrum and the strong Connes spectrum for actions of compact quantum groups on $ C^*$-algebras and obtain necessary and sufficient conditions for a crossed product to be a prime or a simple $ C^*$-algebra. Our results extend to the case of compact quantum actions, namely the results of Gootman, Lazar and Peligrad, which in turn, generalize results by Connes, Olesen, Pedersen and Kishimoto for abelian group actions. We prove in addition that the Connes spectra are closed under tensor products. These results are new for compact nonabelian groups as well.


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Raluca Dumitru
Affiliation: Department of Mathematics and Statistics, University of North Florida, 1 UNF Drive, Jacksonville, Florida 32224 – and – Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Email: raluca.dumitru@unf.edu

Costel Peligrad
Affiliation: Department of Mathematical Sciences, University of Cincinnati, 5514 French Hall West, 2815 Commons Way, Cincinnati, Ohio 45221-0025
Email: costel.peligrad@uc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05562-0
PII: S 0002-9947(2012)05562-0
Received by editor(s): June 6, 2010
Received by editor(s) in revised form: December 28, 2010
Published electronically: March 9, 2012
Additional Notes: The first author was supported by a UNF Summer Research Grant
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.