Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T14:34:43.927Z Has data issue: false hasContentIssue false
  • English
  • Français

A Symmetric Imprimitivity Theorem for Commuting Proper Actions

Published online by Cambridge University Press:  20 November 2018

Astrid an Huef ,
Iain Raeburn  and
Dana P. Williams
Astrid an Huef
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia, e-mail: astrid@unsw.edu.au
Iain Raeburn
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia, e-mail: Iain.Raeburn@newcastle.edu.au
Dana P. Williams
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551, U.S.A., e-mail: dana.williams@dartmouth.edu
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 prove a symmetric imprimitivity theorem for commuting proper actions of locally compact groups $H$ and $K$ on a ${{C}^{*}}$-algebra.

Keywords

Primary: 46L05secondary: 46L0846L55
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 5 , 01 October 2005 , pp. 983 - 1011
Copyright
Copyright © Canadian Mathematical Society 2005

References

[1] Combes, F., Crossed products and Morita equivalence. Proc. LondonMath. Soc. 49(1984), 289–306.Google Scholar
[2] Curto, R. E., Muhly, P. S. and Williams, D. P., Cross products of strongly Morita equivalent C*-algebras. Proc. Amer.Math. Soc. 90(1984), 528–530.Google Scholar
[3] Deicke, K., Pask, D., and Raeburn, I., Coverings of directed graphs and crossed products of C*-algebras by coactions of homogeneous spaces. Internat. J. Math. 14(2003), 773–789.Google Scholar
[4] Dunford, N. and Schwartz, J. T., Linear Operators. I. General Theory. Pure and Applied Mathematics 7, Interscience, New York, 1958.Google Scholar
[5] Echterhoff, S., Kaliszewski, S., Quigg, J., and Raeburn, I., Naturality and induced representations. Bull. Austral. Math. Soc. 61(2000), 415–438.Google Scholar
[6] Echterhoff, S., Kaliszewski, S., and Raeburn, I., Crossed products by dual coactions of groups and homogeneous spaces. J. Operator Theory 39(1998), 151–176.Google Scholar
[7] Exel, R., Morita-Rieffel equivalence and spectral theory for integrable automorphism groups of C*-algebras, J. Funct. Anal. 172(2000), 404–465.Google Scholar
[8] Fell, J. M. G. and Doran, R., Representations of*-Algebras, Locally Compact Groups, and Banach*-Algebraic Bundles. Vol. I & II, Academic Press, New York, 1988.Google Scholar
[9] Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis. I. Second edition, Grundlehren der MathematischenWissenschaften 115, Springer-Verlag, Berlin, 1979.Google Scholar
[10] an Huef, A. and Raeburn, I., Mansfield's imprimitivity theorem for arbitrary closed subgroups. Proc. Amer.Math. Soc. 132(2004), 1153–1162.Google Scholar
[11] an Huef, A. and Raeburn, I., Regularity of induced representations and a theorem of Quigg and Spielberg. Math. Proc. Cambridge Philos. Soc. 133(2002), 249–259.Google Scholar
[12] an Huef, A., Raeburn, I., and Williams, D. P., An equivariant Brauer semigroup and the symmetric imprimitivity theorem. Trans. Amer.Math. Soc. 352(2000), 4759–4787.Google Scholar
[13] an Huef, A., Raeburn, I., and Williams, D. P., Proper actions on imprimitivity bimodules and decompositions of Morita equivalences. J. Funct. Anal. 200(2003), 401–428.Google Scholar
[14] Kasparov, G. G., Equivariant KK-theory and the Novikov conjecture. Invent.Math. 91(1988), 147–201.Google Scholar
[15] Kaliszewski, S. and Quigg, J., Imprimitivity for C*-coactions of non-amenable groups. Math. Proc. Cambridge Philos. Soc. 123(1998), 101–118.Google Scholar
[16] Mansfield, K., Induced representations of crossed products by coactions. J. Funct. Anal. 97(1991), 112–161.Google Scholar
[17] Meyer, R., Equivariant Kasparov theory and generalized homomorphisms. K-Theory 21(2000), 201–228.Google Scholar
[18] Meyer, R., Generalized fixed point algebras and square-integrable group actions. J. Funct. Anal. 186(2001), 167–195.Google Scholar
[19] Pask, D. and Raeburn, I., Symmetric imprimitivity theorems for graph C*-algebras. Internat. J. Math. 12(2001), 609–623.Google Scholar
[20] Raeburn, I., Induced C*-algebras and a symmetric imprimitivity theorem. Math. Ann. 280(1988), 369–387.Google Scholar
[21] Raeburn, I., On crossed products by coactions and their representation theory. Proc. LondonMath. Soc. 64(1992), 625–652.Google Scholar
[22] Raeburn, I. and Williams, D. P., Morita Equivalence and Continuous-Trace C*-Algebras. Mathematical Surveys and Monographs 60, American Mathematical Society, Providence, RI, 1998.Google Scholar
[23] Rieffel, M. A., Applications of strong Morita equivalence to transformation group C*-algebras. In: Operator Algebras and Applications, Proc. Symp. Pure Math. 38, American Mathematical Society, Providence, RI, 1982, pp. 299–310.Google Scholar
[24] Rieffel, M. A., Proper actions of groups on C*-algebras. In: Mappings of Operator Algebras, Progr.Math. 84, Birkhauser, Boston, 1990, pp. 141–182.Google Scholar
[25] Rieffel, M. A., Integrable and proper actions on C*-algebras, and square integrable representations of groups. Expo. Math. 22(2004), 1–53.Google Scholar