Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T13:43:43.630Z Has data issue: false hasContentIssue false
  • English
  • Français

Discrete coactions on C*-algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

Chi-Keung Ng
Chi-Keung Ng
Affiliation:
Mathematical InstituteUniversity of Oxford24–29 St. Giles Oxford OX1 3LB, England
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 will consider coactions of discrete groups on C*-algebras and imitate some of the results about compact group actions on C*-algebras. In particular, the crossed product of a reduced coaction ∈ of a discrete amenable group G on A is liminal (respectively, postliminal) if and only if the fixed point algebra of ∈ is. Moreover, we will also consider ergodic coactions on C*-algebras.

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 1 , February 1996 , pp. 118 - 127
Copyright
Copyright © Australian Mathematical Society 1996

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]Gootman, E. C. and Lazar, A. J., ‘Applications of non-commutative duality to crossed product C*-algebras determined by actions or coactions’, Proc. London Math. Soc. 59 (1989), 593–624.CrossRefGoogle Scholar
[3]Gootman, E. C. and Lazar, A. J., ‘Compact group actions on C*-algebras: An application of non-commutative duality’, J. Funct. Anal. 91 (1990), 237–245.CrossRefGoogle Scholar
[4]Green, P., ‘The local structure of twisted covariance algebras’, Acta Math. 140 (1978), 191–250.CrossRefGoogle Scholar
[5]Hoegh-Krohn, R., Landstad, M. B. and Stormer, E., ‘Compact ergodic groups of automorphisms’, Ann. of Math. 114 (1981), 75–86.CrossRefGoogle Scholar
[6]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.CrossRefGoogle Scholar
[7]Katayama, Y., ‘Takesaki's duality for a nondegenerate coaction’, Math. Scand. 55 (1985), 141–151.CrossRefGoogle Scholar
[8]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
[9]Quigg, J. C., ‘Landstad duality for C*-coactions’, to appear.Google Scholar
[10]Quigg, J. C., ‘Discrete homogeneous C*-coactions’, preprint.Google Scholar
[11]Reaburn, I., ‘A duality theorem for crossed products by nonabelian groups’, Proc. Centre Math. Anal. Austral. Nat. Univ. 15 (1987), 214–227.Google Scholar
[12]Raeburn, I., ‘On crossed products by coactions and their representation theory’, Proc. London Math. Soc. (3) 64 (1992), 625–652.CrossRefGoogle Scholar