Spectra for compact quantum group coactions and crossed products
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. © 2012 American Mathematical Society.
Transactions of the American Mathematical Society
Digital Object Identifier (DOI)
Dumitru, & Peligrad, C. (2012). Spectra for compact quantum group coactions and crossed products. Transactions of the American Mathematical Society, 364(7), 3699–3713. https://doi.org/10.1090/S0002-9947-2012-05562-0