Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-17T02:34:11.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Twisted crossed products of C*-algebras

Published online by Cambridge University Press:  28 June 2011

Judith A. Packer  and
Iain Raeburn
Judith A. Packer
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 0511
Iain Raeburn
Affiliation:
School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, NSW 2033, Australia and Department of Mathematics, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
Get access Rights & Permissions [Opens in a new window]

Extract

Group algebras and crossed products have always played an important role in the theory of C*-algebras, and there has also been considerable interest in various twisted analogues, where the multiplication is twisted by a two-cocycle. Here we shall discuss a very general family of twisted actions of locally compact groups on C*-algebras, and the corresponding twisted crossed product C*-algebras. We shall then establish some of the basic properties of these algebras, motivated by the requirements of some applications we have in mind [2, 9, 10]. Some of our results will be known to others, at least in principle, but we feel that a coherent account might be useful.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 293 - 311
Copyright
Copyright © Cambridge Philosophical Society 1989

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

[1] Busby, R. C. and Smith, H. A.. Representations of twisted group algebras. Trans. Amer. Math. Soc. 149 (1970), 503–537.CrossRefGoogle Scholar
[2] Crocker, D., Kumjian, A. and Raeburn, I.. An equivariant Brauer group and actions of groups on C*-algebras. (In preparation.)Google Scholar
[3] Brabanter, M. De. Decomposition theorems for certain C*-crossed products. Math. Proc. Cambridge Philos. Soc. 94 (1983), 265–275.CrossRefGoogle Scholar
[4] Doran, R. S. and Wichmann, J.. Approximate Identities and Factorisation in Banach Modules. Lecture Notes in Math. vol. 768 (Springer-Verlag, 1979).Google Scholar
[5] Green, P.. The local structure of twisted covariance algebras. Acta Math. 140 (1978), 191–250.CrossRefGoogle Scholar
[6] Hille, E. and Phillips, R. S.. Functional Analysis and Semigroups (American Mathematical Society, 1957).Google Scholar
[7] Leptin, H.. Darstellungen verallgemeinerter L1-Algebren. Invent. Math. 5 (1968), 192–215.CrossRefGoogle Scholar
[8] Moore, C. C.. Group extensions and cohomology for locally compact groups, III. Trans. Amer. Math. Soc. 221 (1976), 1–33.CrossRefGoogle Scholar
[9] Olesen, D. and Raeburn, I.. Pointwise unitary automorphism groups. (Submitted.)Google Scholar
[10] Packer, J. and Raeburn, I.. The structure of twisted group C*-algebras. (Submitted.)Google Scholar
[11] Pedersen, G. K.. C*-algebras and their Automorphism Groups (Academic Press, 1979).Google Scholar
[12] Quigg, J. C.. Duality for reduced twisted crossed products of C*-algebras. Indiana Univ. Math. J. 35 (1986), 549–571.CrossRefGoogle Scholar
[13] Raeburn, I.. On crossed products and Takai duality. Proc. Edinburgh Math. Soc. 31 (1988), 321–330.CrossRefGoogle Scholar
[14] Raeburn, I.. A duality theorem for crossed products by non-abelian groups. Proc. Centre Math. Anal. Austral. Nat. Univ. 15 (1987), 214–227.Google Scholar
[15] Reed, M. and Simon, B.. Functional Analysis (Academic Press, 1972).Google Scholar
[16] Yoshida, K.. Functional Analysis (Springer-Verlag, 1974).CrossRefGoogle Scholar
[17] Zeller-Meier, G.. Produits croisés d'une C*-algèbre par un group d'automorphismes. J. Math. Pures Appl. 47 (1968), 101–239.Google Scholar