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Exotic Coactions

Landstad, Magnus B.; Kaliszewski, Steve; Quigg, John
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2462273
Date
2016
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  • Institutt for matematiske fag [2675]
  • Publikasjoner fra CRIStin - NTNU [41881]
Original version
Proceedings of the Edinburgh Mathematical Society. 2016, 59 (2), 411-434.   10.1017/S0013091515000164
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).
Publisher
Cambridge University Press (CUP)
Journal
Proceedings of the Edinburgh Mathematical Society

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