Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T00:38:21.314Z Has data issue: false hasContentIssue false
  • English
  • Français

Discrete coactions on Hilbert C*-modules

Published online by Cambridge University Press:  24 October 2008

Chi-Keung Ng
Chi-Keung Ng
Affiliation:
Mathematical Institute, 24–29 St Giles, Oxford OX1 3LB e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper, we will investigate discrete coactions on Hilbert C*-modules. In particular, we obtain a one-to-one correspondence between Hilbert C*-modules with discrete coactions and Hilbert C*-modules over the crossed products of the original C*-algebras which satisfies some nice properties (see 3·6 and 3·7). Then we will give some applications of this correspondence in the last three sections.

In Section 2, we give some results about discrete coactions on Hilbert C*-modules which mainly correspond to those about discrete coactions on C*-algebras (see [7]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 103 - 112
Copyright
Copyright © Cambridge Philosophical Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Blackadar, B.. K-theory for operator algebras. M.S.R.I. Publications 5 (Springer-Verlag, 1986).CrossRefGoogle Scholar
[2]Baaj, S. and Skandalis, G.. C*-algèbres de Hopf et théorie de Kasparov équivariante. K-theory 2 (1989), 683–721.CrossRefGoogle Scholar
[3]Jensen, K. K. and Thomsen, K.. Elements of KK-theory (Birkhauser, 1991).CrossRefGoogle Scholar
[4]Kasparov, G. G.. Equivariant KK-theory and the Novikov conjecture. Invent. Math. 91 (1988), 147–201.CrossRefGoogle 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]Mingo, J. and Phillips, J.. Equivariant triviality theorem for Hilbert C*-modules. Proc. Amer. Math. Soc. 91 (1984) 225–230.Google Scholar
[7]Ng, C. K.. Discrete coactions on C*-algebras, to appear in J. Aust. Math. Soc.Google Scholar
[8]Phillips, N. C.. Equivariant K-theory for proper actions. Pit. Res. Notes in Math. Ser. 178 (1989).Google Scholar
[9]Quigg, J.. Discrete homogeneous C*-coactions (preprint).Google Scholar
[10]Raeburn, I.. On crossed products by coactions and their representation theory. Proc. London Math. Soc. (3) 64 (1992), 625–652.CrossRefGoogle Scholar
[11]Takesaki, M.. Theory of operator algebras I (Springer-Verlag, 1979).CrossRefGoogle Scholar
[12]Vallin, J. M.. C*-algèbres de Hopf et C*-algèbres de Kac. Proc. London Math. Soc. (3) 50 (1985), 131–174.CrossRefGoogle Scholar