Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T13:37:23.760Z Has data issue: false hasContentIssue false
  • English
  • Français

Full and reduced C*-coactions

Published online by Cambridge University Press:  24 October 2008

John C. Quigg
John C. Quigg
Affiliation:
Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Full and reduced C*-coactions are shown to be essentially equivalent as far as the representations and cocrossed products are concerned, at least in the presence of non-degeneracy. This is shown to be particularly true for a special class of full coactions which are given the name normal.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 3 , November 1994 , pp. 435 - 450
Copyright
Copyright © Cambridge Philosophical Society 1994

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

[BS]Baaj, S. and Skandalis, G.. C*-algèbres de Hopf et théorie de Kasparov équivariante. K-theory 2 (1989), 683–721.CrossRefGoogle Scholar
[Eno]Enock, M.. Produit croisé d'une algèbre de von Neumann par une algèbre de Kac. J. Funet. Anal. 26 (1977), 16–47.CrossRefGoogle Scholar
[ES]Enock, E. and Schwartz, J.-M.. Produit croisé d'une algèbre de von Neumann par une algèbre de Kac. II. Publ. Res. Inst. Math. Sci. 16 (1980), 189–232.CrossRefGoogle Scholar
[IT]Imai, S. and Takai, H.. On a duality for C*-crossed products by a locally compact group. J. Math. Soc. Japan 30 (1978), 495–504.Google Scholar
[Ior]Iorio, V.. Hopf-C*-algebras and locally compact groups. Pacific J. Math. 87 (1980), 75–96.CrossRefGoogle Scholar
[Lan]Landstad, M. B.. Duality for covariant systems. Trans. Amer. Math. Soc. 248 (1979), 223–267.CrossRefGoogle Scholar
[Kat]Katayama, Y.. Takesaki's duality for a non-degenerate co-action. Math. Scand. 55 (1985), 141–151.CrossRefGoogle Scholar
[LPRS]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
[Nak]Nakagami, Y.. Dual action on a von Neumann algebra and Takesaki's duality for a locally compact group. Publ. Res. Inst.Math. Sci. 12 (1977), 727–775.CrossRefGoogle Scholar
[NT]Nakagami, Y. and Takesaki, M.. Duality for crossed products of von Neumann algebras. Lecture Notes in Math., vol. 731 (Springer-Verlag, 1979).CrossRefGoogle Scholar
[Qui1]Quigg, J. C.. Full C*-crossed product duality. J. Austral. Math. Soc. Ser. A 50 (1991), 34–52.CrossRefGoogle Scholar
[Qui2]Quigg, J. C.. Landstad duality for C*-coactions. Math. Scand., to appear.Google Scholar
[QR]Quigg, J. C. and Raeburn, I.. Induced C*-algebras and Landstad duality for twisted C*-coactions, preprint.Google Scholar
[Rae1]Raeburn, I.. A duality theorem for crossed products by nonabelian groups. Pror. Centre Math. Anal. Austral. Nat. Univ. 15 (1987), 214–227.Google Scholar
[Rae2]Raeburn, I.. On crossed products by coactions and their representation theory. Proc. London Math. Soc. (3) 64 (1992), 625–652.CrossRefGoogle Scholar
[SVZ]Strätilä, S., Voiculescu, D. and Zsidó, L.. On crossed products. I, Rev. Roumaine Math. Pures Appl. 21 (1976), 1411–1449; II, Rev. Roumaine Math. Pures Appl. 22 (1977), 83–117.Google Scholar
[Tak]Takai, H.. On a duality for crossed products of C*-algebras. J. Funct. Anal. 19 (1975), 25–39.CrossRefGoogle Scholar
[Val]Vallin, J.-M.. C*-algèbres de Hopf et C*-algèbres de Kac. Proc. London Math. Soc. (3) 50 (1985), 131–174.CrossRefGoogle Scholar