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Exotic Coactions

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 March 2016

S. Kaliszewski ,
Magnus B. Landstad  and
John Quigg
S. Kaliszewski
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA ([email protected]; [email protected])
Magnus B. Landstad
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway ([email protected])
John Quigg
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA ([email protected]; [email protected])
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Abstract

If a locally compact group G acts on a C*-algebra B, we have both full and reduced crossed products and each has a coaction of G. We investigate ‘exotic’ coactions in between the two, which are determined by certain ideals E of the Fourier–Stieltjes algebra B(G); an approach that is inspired by recent work of Brown and Guentner on new C*-group algebra completions. We actually carry out the bulk of our investigation in the general context of coactions on a C*-algebra A. Buss and Echterhoff have shown that not every coaction comes from one of these ideals, but nevertheless the ideals do generate a wide array of exotic coactions. Coactions determined by these ideals E satisfy a certain ‘E-crossed product duality’, intermediate between full and reduced duality. We give partial results concerning exotic coactions with the ultimate goal being a classification of which coactions are determined by ideals of B(G).

Keywords

group C*-algebracoactionC*-bialgebraFourier–Stieltjes algebra

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 411 - 434
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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