Spectra for compact quantum group coactions and crossed products

Dumitru, Raluca; Peligrad, Costel

doi:10.1090/S0002-9947-2012-05562-0

Spectra for compact quantum group coactions and crossed products
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by Raluca Dumitru and Costel Peligrad PDF

Trans. Amer. Math. Soc. 364 (2012), 3699-3713 Request permission

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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