Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-20T00:44:27.885Z Has data issue: false hasContentIssue false
  • English
  • Français

Full coactions on Hilbert C*-modules

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Huu Hung Bui
Huu Hung Bui
Affiliation:
School of MPCE MacquarieUniversity SydneyNSW 2109, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We introduce a natural notion of full coactions of a locally compact group on a Hilbert C*-module, and associate each full coaction in a natural way to an ordinary coaction. We also introduce a natural notion of strong Morita equivalence of full coactions which is sufficient to ensure strong Morita equivalence of the corresponding crossed product C*-algebras.

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 46L60: Applications of selfadjoint operator algebras to physics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 409 - 420
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Baaj, S. and Skandalis, G., ‘C*-algèbres de Hopf et théorie de Kasparov équivariante’, K-theory 2 (1989), 683–721.CrossRefGoogle Scholar
[2]Blackadar, B., K-theory for operator algebras, Math. Sci. Research Inst. Pub. (Springer, New York, 1986).CrossRefGoogle Scholar
[3]Bui, H. H., ‘Morita equivalence of twisted crossed products by coactions’, J. Funct. Anal. 123 (1994), 59–98.CrossRefGoogle Scholar
[4]Kasparov, G. G., ‘Hilbert C*-modules: theorem of Stinespring and Voiculescu’, J. Operator Theory 4 (1980), 133–150.Google Scholar
[5]Landstad, M. B., Phillips, J., Raeburn, I. and Sutherland, C. E., ‘Representations of crossed products by coactions and principal bundles’, Trans. Amer. Math. Soc. 299 (1987), 747–784.CrossRefGoogle Scholar
[6]Raeburn, I., ‘On crossed products by coactions and their representation theory’, Proc. London Math. Soc. 64 (1992), 625–652.CrossRefGoogle Scholar
[7]Rieffel, M. A., ‘Induced representations of C*-algebras’, Adv. Math. 13 (1974), 176–257.CrossRefGoogle Scholar
[8]Rieffel, M. A., ‘Unitary representations of group extension; an algebraic approach to the theory of Mackay and Blattner’, in: Studies in analysis, Advances in Math., Suppl. Studies 4(Academic Press, New York, 1979)pp. 43–82.Google Scholar
[9]Thomsen, K., Hilbert C*-modules, KK-theory and C*-extensions, Various Publication Series 43 (Acahus Universitet, Aarhus, 1988).Google Scholar