Spectra for compact quantum group coactions and crossed products

Document Type

Article

Publication Date

3-9-2012

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. © 2012 American Mathematical Society.

Publication Title

Transactions of the American Mathematical Society

Volume

364

Issue

7

First Page

3699

Last Page

3713

Digital Object Identifier (DOI)

10.1090/S0002-9947-2012-05562-0

ISSN

00029947

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