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C*-actions of r-discrete groupoids and inverse semigroups

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

John Quigg  and
Nándor Sieben
John Quigg
Affiliation:
Department of Mathematics, Arizona State University, Tempe, Arizona 85287 e-mail: [email protected], nandor.sieben@:1:28 asu.edu
Nándor Sieben
Affiliation:
Department of Mathematics, Arizona State University, Tempe, Arizona 85287 e-mail: [email protected], nandor.sieben@:1:28 asu.edu
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Abstract

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Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.

MSC classification

Secondary: 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 2 , April 1999 , pp. 143 - 167
Copyright
Copyright © Australian Mathematical Society 1999

References

[Bla]Blanchard, E., ‘Déformation de C*-algèbres de Hopf’, Bull. Soc. Math. France 124 (1996), 141–215.Google Scholar
[Dix]Dixmier, J., C*-algebras (North-Holland, Amsterdam, 1977).Google Scholar
[DG]Dupré, M. J. and Gillette, R. M., Banach bundles, Banach modules and automorphisms of C*-algebras, Res. Notes Math. Ser. 92 (Pitman, 1983).Google Scholar
[Exe]Exel, R., ‘Circle actions on C*-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence’, J. Funct. Anal. 122 (1994), 361–401.CrossRefGoogle Scholar
[Exe]Exel, R., ‘Partial actions of groups and actions of inverse semigroups’, Proc. Amer. Math. Soc., to appear.Google Scholar
[Hae]Haefliger, A., ‘Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes’, Comment. Math. Helv. 32 (1958), 248–329.CrossRefGoogle Scholar
[HR]Hancock, R. and Raeburn, I., ‘The C*-algebras of some inverse semigroups’, Bull. Austral. Math. Soc. 42 (1990), 335–348.CrossRefGoogle Scholar
[Kum1]Kumjian, A., ‘On localizations and simple C*-algebras’, Pacific J. Math. 112 (1984), 141–192.CrossRefGoogle Scholar
[Kum2]Kumjian, A., ‘Fell bundles over groupoids’, Proc. Amer. Math. Soc. 126 (1998), 1115–1125.CrossRefGoogle Scholar
[McC]McClanahan, K., ‘K-theory for partial crossed products by discrete groups’, J. Funct. Anal. 130 (1995), 77–117.CrossRefGoogle Scholar
[Nic]Nica, A., ‘On a groupoid construction for actions of certain inverse semigroups’, Internat. J. Math. 5 (1994), 349–372.CrossRefGoogle Scholar
[Nil]Nilsen, M., ‘C*-bundles and C0(X)-algebras’, Indiana Univ. Math. J. 45 (1996), 463–478.CrossRefGoogle Scholar
[Pat]Paterson, A. L. T., Groupoids, inverse semigroups, and their operator algebras (Birkhäuser, to appear).CrossRefGoogle Scholar
[Rae]Raeburn, I., ‘Induced C*-algebras and a symmetric imprimitivity theorem’, Math. Ann. 280 (1988), 369–387.CrossRefGoogle Scholar
[Rei]Reinhart, B. L., Geometry of foliations, Ergebnisse der Mathematik und ihrer Grenzgebiete, 99 (Springer, Berlin, 1983).CrossRefGoogle Scholar
[Ren1]Renault, J. N., A groupoid approach to C*-algebras, Lecture Notes in Math., 793 (Springer, Berlin, 1980).CrossRefGoogle Scholar
[Ren2]Renault, J. N., ‘Représentation des produits croisés d'algèbres de groupoides’, J. Operator Theory 18 (1987), 67–97.Google Scholar
[Rie]Rieffel, M. A., ‘Continuous fields of C*-algebras coming from group cocycles and actions’, Math. Ann. 283 (1989), 531–562.CrossRefGoogle Scholar
[Sie1]Sieben, N., Actions of inverse semigroups on C*-algebras (Ph.D. Thesis, Arizona State University, 1997).Google Scholar
[Sie2]Sieben, N., ‘C*-crossed products by partial actions and actions of inverse semigroups’, J. Austral. Math. Soc. Ser. A 63 (1997), 32–46.CrossRefGoogle Scholar