Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T14:20:30.516Z Has data issue: false hasContentIssue false
  • English
  • Français

Full C*-Crossed product duality

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

John C. Quigg
John C. Quigg
Affiliation:
Department of Mathematics Arizona State University Tempe, Arizona 85287, U.S.A.
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.

Takai duality for full C*-crossed products holds for twisted actions in the sense of Green and fails for coactions.

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 1 , February 1991 , pp. 34 - 52
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Busby, R. C. and Smith, H. A., ‘Representations of twisted group algebras,’ Trans. Amer. Math. Soc. 132 (1968), 79–99.Google Scholar
[2]Gootman, E. C. and Lazar, A. J., ‘Applications of non-commutative duality to crossed product C *-algebras determined by an action or coaction’, preprint.Google Scholar
[3]Green, P., ‘The local structure of twisted covariance algebras’, Acta. Math. 140 (1978), 191–250.CrossRefGoogle Scholar
[4]Green, P., ‘The structure of imprimitivity algebras,’ J. Funct. Anal. 36 (1980), 88–104.CrossRefGoogle Scholar
[5]Katayama, Y., ‘Takesaki's duality for a non-degenerate co-action,’ Math. Scand. 55 (1985), 141–151.CrossRefGoogle Scholar
[6]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
[7]Mansfield, K., Induced representations of crossed products by coactions, (dissertation, Univ. N. S. W., Sydney, Australia).Google Scholar
[8]Mansfield, K., ‘Induced representations of crossed products by coactions,’ Proc. Cent. Math. Anal. Austral. Nat. Univ. 17 (1988), 191–196.Google Scholar
[9]Packer, J. A. and Raeburn, I., ‘Twisted crossed products of C *-algebras,’ preprint.Google Scholar
[10]Pedersen, G. K., C*-algebras and their automorphism groups, (Academic Press, New York, 1979).Google Scholar
[11]Quigg, J. C., ‘Duality for reduced twisted crossed products of C *-algebras,’ Indiana Univ. Math. J. 35 (1986), 549–571.CrossRefGoogle Scholar
[12]Raeburn, I., ‘A duality theorem for crossed products by nonabelian groups,’ Proc. Cent. Math. Anal. Austral. Nat. Univ. 15 (1987), 214–227.Google Scholar
[13]Rieffel, M. A., ‘Induced representations of C *-algebras,’ Adv. in Math. 13 (1974), 176–257.CrossRefGoogle Scholar