## Mansfield’s imprimitivity theorem for arbitrary closed subgroups

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- by Astrid an Huef and Iain Raeburn PDF
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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 $H$.## References

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## Additional Information

**Astrid an Huef**- Affiliation: School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
- MR Author ID: 620419
- 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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**132**(2004), 1153-1162 - MSC (2000): Primary 46L05; Secondary 46L08, 46L55
- DOI: https://doi.org/10.1090/S0002-9939-03-07189-2
- MathSciNet review: 2045432