Duality of restriction and induction for $C^*$-coactions
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- by S. Kaliszewski, John Quigg and Iain Raeburn PDF
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Abstract:
Consider a coaction $\delta$ of a locally compact group $G$ on a $C^*$ algebra $A$, and a closed normal subgroup $N$ of $G$. We prove, following results of Echterhoff for abelian $G$, that Mansfield’s imprimitivity between $A\times _{\delta |}G/N$ and $A\times _\delta G\times _{\hat \delta ,r}N$ implements equivalences between Mansfield induction of representations from $A\times _{\delta |}G/N$ to $A\times _\delta G$ and restriction of representations from $A\times _\delta G\times _{\hat \delta ,r}N$ to $A\times _\delta G$, and between restriction of representations from $A\times _\delta G$ to $A\times _{\delta |}G/N$ and Green induction of representations from $A\times _\delta G$ to $A\times _\delta G\times _{\hat \delta ,r}N$. This allows us to deduce properties of Mansfield induction from the known theory of ordinary crossed products.References
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Additional Information
- S. Kaliszewski
- Affiliation: Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, Australia
- MR Author ID: 341615
- Email: kaz@frey.newcastle.edu.au
- John Quigg
- Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287
- MR Author ID: 222703
- Email: quigg@math.la.asu.edu
- Iain Raeburn
- Affiliation: Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, Australia
- Email: iain@frey.newcastle.edu.au
- Received by editor(s): December 11, 1995
- Additional Notes: This research was partially supported by the National Science Foundation under Grant No. DMS9401253, and by the Australian Research Council.
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 2085-2113
- MSC (1991): Primary 46L55
- DOI: https://doi.org/10.1090/S0002-9947-97-01905-3
- MathSciNet review: 1407703