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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mansfield's imprimitivity theorem for arbitrary closed subgroups


Authors: Astrid an Huef and Iain Raeburn
Journal: Proc. Amer. Math. Soc. 132 (2004), 1153-1162
MSC (2000): Primary 46L05; Secondary 46L08, 46L55
Published electronically: August 28, 2003
MathSciNet review: 2045432
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Abstract: Let $\delta$ be a nondegenerate coaction of $G$ on a $C^*$-algebra $B$, and let $H$be a closed subgroup of $G$. The dual action $\hat\delta:H\to\operatorname{Aut}(B\times_\delta G)$ is proper and saturated in the sense of Rieffel, and the generalised fixed-point algebra is the crossed product of $B$ by the homogeneous space $G/H$. The resulting Morita equivalence is a version of Mansfield's imprimitivity theorem which requires neither amenability nor normality of $H$.


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Additional Information

Astrid an Huef
Affiliation: School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
Email: astrid@maths.unsw.edu.au

Iain Raeburn
Affiliation: School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia
Email: iain@frey.newcastle.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07189-2
PII: S 0002-9939(03)07189-2
Received by editor(s): June 30, 2002
Received by editor(s) in revised form: December 18, 2002
Published electronically: August 28, 2003
Additional Notes: This research was supported by grants from the Australian Research Council, the University of New South Wales and the University of Newcastle.
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society