Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T04:19:40.953Z Has data issue: false hasContentIssue false
  • English
  • Français

Discrete C*-coactions and C*-algebraic bundles

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

John C. Quigg
John C. Quigg
Affiliation:
Department of MathematicsArizona State UniversityTemkpe, Arizona 85287USA e-mail: [email protected]
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.

Discrete C*-coactions are shown to be equivalent to discrete C* -algebraic bundles. Simplicity, primeness, liminality, postliminality, and nuclearity are related to the fixed point algebra and the cocrossed product. Ergodic, and more generally homogeneous, C*-coactions are characterized.

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 2 , April 1996 , pp. 204 - 221
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]Beer, W., ‘On Morita equivalence of nuclear C*-algebras’, J. Pure Appl. Algebra 26 (1982), 249–267.CrossRefGoogle Scholar
[3]Brown, L. G., Green, P. and Rieffel, M. A., ‘Stable isomorphism and strong Morita equivalence of C*-algebras’, Pacific J. Math. 71 (1977), 349–363.CrossRefGoogle Scholar
[4]Busby, R. C. and Smith, H. A., ‘Representations of twisted group algebras’, Trans. Amer. Math. Soc. 149 (1970), 503–537.CrossRefGoogle Scholar
[5]Exel, Ruy, ‘Circle actions on C*-algebras, Partial automorphisms and a generalized Pimsner-Voiculescu exact sequence’, J. Funct. Anal. 122 (1994), 361–401.CrossRefGoogle Scholar
[6]Fell, J. M. G., An extension of Mackey's method to Banach*-algebraic bundles, Mem. Amer. Math. Soc. 90 (Amer. Math. Soc., Providence, 1969).Google Scholar
[7]Fell, J. M. G. and Doran, R. S., Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles (Academic Press, Boston, 1988).Google Scholar
[8]Green, P., ‘The local structure of twisted convariance algebras’, Acta Math. 140 (1978), 191–250.CrossRefGoogle Scholar
[9]Katayama, Y., ‘Takesaki's duality for a non-degenerate co-action’, Math. Scand. 55 (1985), 141–151.CrossRefGoogle Scholar
[10]Katayama, Y. and Song, G., ‘Ergodic co-actions of discrete groups’, Math. japon. 27 (1982), 159–175.Google Scholar
[11]Kishimoto, A. and Takai, H., ‘Some remarks on C*-dynamical systems with a compact abelian group’, Publ. Res. Inst. Math. Sci. 14 (1978), 383–397.CrossRefGoogle Scholar
[12]Landstad, M. B., ‘Algebras of spherical functions associated with covariant systems over a compact group’, Math. Scand. 47 (1980), 137–149.CrossRefGoogle Scholar
[13]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
[14]Leptin, H., ‘Verallgemeinerte L 1-algebren’, Math. Ann. 159 (1965), 51–76.CrossRefGoogle Scholar
[15]Ng, C. K., ‘Discrete coactions on C*-algebras’, J. Austral. Math. Soc. (Ser. A) 60 (1996), 118–127.CrossRefGoogle Scholar
[16]Olesen, D., Pedersen, G. K. and Takesaki, M., ‘Ergodic actions of compact abelian groups’, J. Operator Theory 3 (1980), 237–269.Google Scholar
[17]Packer, J. A. and Raeburn, I., ‘Twisted crossed products of C*-algebras’, Math. Proc. Cambridge Philos. Soc. 106 (1989), 293–311.CrossRefGoogle Scholar
[18]Peligrad, C., ‘Locally compact group actions on C*-algeras and compact subgroups’, J. Funct. Anal. 76 (1988), 126–139.CrossRefGoogle Scholar
[19]Quigg, J. C., ‘Full and reduced C*-coactions’, Math. Proc. Cambridge Philos. Soc. 116 (1994), 435–450.CrossRefGoogle Scholar
[20]Quigg, J. C., ‘Full C*-crossed product duality’, J. Austral. Math. Soc. (Ser. A) 50 (1991), 34–52.CrossRefGoogle Scholar
[21]Raeburn, I., ‘On crossed products by coactions and their representation theory’, Proc. London Math. Soc. (3) 64 (1992), 625–652.CrossRefGoogle Scholar
[22]Rieffel, M. A., ‘Induced representations of C*-algebras’, Adv. Math. 13 (1974), 176–257.CrossRefGoogle Scholar