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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Duality of restriction
and induction for $C^*$-coactions


Authors: S. Kaliszewski, John Quigg and Iain Raeburn
Journal: Trans. Amer. Math. Soc. 349 (1997), 2085-2113
MSC (1991): Primary 46L55
MathSciNet review: 1407703
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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.


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Additional Information

S. Kaliszewski
Affiliation: Department of Mathematics, University of Newcastle, Newcastle, New South Wales 2308, Australia
Email: kaz@frey.newcastle.edu.au

John Quigg
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287
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

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01905-3
PII: S 0002-9947(97)01905-3
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.
Article copyright: © Copyright 1997 American Mathematical Society