Duality of restriction

and induction for -coactions

Authors:
S. Kaliszewski, John Quigg and Iain Raeburn

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider a coaction of a locally compact group on a - algebra , and a closed normal subgroup of . We prove, following results of Echterhoff for abelian , that Mansfield's imprimitivity between and implements equivalences between Mansfield induction of representations from to and restriction of representations from to , and between restriction of representations from to and Green induction of representations from to . 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:
https://doi.org/10.1090/S0002-9947-97-01905-3

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