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Three bimodules for Mansfield's imprimitivity theorem

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

S. Kaliszewski  and
John Quigg
S. Kaliszewski
Affiliation:
Department of Mathematics, Arizona State University, Tempe AZ 85287, USA e-mail: kaliszewski@asu.edu e-mail: quigg@asu.edu
John Quigg
Affiliation:
Department of Mathematics, Arizona State University, Tempe AZ 85287, USA e-mail: kaliszewski@asu.edu e-mail: quigg@asu.edu
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Abstract

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For a maximal coaction δ of a discrete group G on a C*-algebra A and a normal subgroup N of G, there are at least three natural A × G ×δ| N - A ×δ|1 G/N imprimitivity bimodules: Mansfield's bimodule ; the bimodule assembled by Ng from Green's imprimitivity bimodule and Katayama duality; and the bimodule assembled from and the crossed-product Mansfield bimodule . We show that all three of these are isomorphic, so that the corresponding inducing maps on representations are identical. This can be interpreted as saying that Mansfield and Green induction are inverses of one another ‘modulo Katayama duality’. These results pass to twisted coactions; dual results starting with an action are also given.

Keywords

C*-algebracoactionduality

MSC classification

Secondary: 46L55: Noncommutative dynamical systems

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 3 , December 2001 , pp. 397 - 420
Copyright
Copyright © Australian Mathematical Society 2001

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