Exotic Coactions
Journal article, Peer reviewed
Accepted version
Permanent lenke
http://hdl.handle.net/11250/2462273Utgivelsesdato
2016Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2351]
- Publikasjoner fra CRIStin - NTNU [37215]
Originalversjon
Proceedings of the Edinburgh Mathematical Society. 2016, 59 (2), 411-434. 10.1017/S0013091515000164Sammendrag
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).