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On partial actions and groupoids
Author(s):
Fernando
Abadie
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1037-1047.
MSC (2000):
Primary 46L05
Posted:
November 7, 2003
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Abstract:
We prove that, as in the case of global actions, any partial action gives rise to a groupoid provided with a Haar system, whose  -algebra agrees with the crossed product by the partial action.
References:
-
- 1.
- F. Abadie, Enveloping actions and Takai duality for partial actions, J. Funct. Anal. 197 (2003), 14-67.
- 2.
- R. Exel, Circle actions on
 -algebras, partial automorphisms and a generalized Pimsner-Voiculescu exact sequence, J. Funct. Anal. 122 (1994), 361-401. MR 95g:46122 - 3.
- R. Exel, The Bunce-Deddens algebras as crossed products by partial automorphisms, Bol. Soc. Brasil. Mat. 25 (2) (1994), 173-179. MR 95m:46091
- 4.
- R. Exel, Approximately finite
 -algebras and partial automorphisms, Math. Scand. 77 (1) (1995), 281-288. MR 97e:46085 - 5.
- R. Exel, Twisted partial actions, a classification of regular
 -algebraic bundles, Proc. London Math. Soc. 74 (1997), 417-443. MR 98d:46075 - 6.
- R. Exel, Partial actions of groups and actions of inverse semigroups, Proc. Amer. Math. Soc. 126 (1998), no. 12, 3481-3494. MR 99b:46102
- 7.
- R. Exel and M. Laca, Cuntz-Krieger algebras for infinite matrices, J. Reine Angew. Math. 512 (1999), 119-172. MR 2000i:46064
- 8.
- R. Exel, M. Laca, and J. Quigg, Partial dynamical systems and
 -algebras generated by partial isometries, J. Operator Theory 47 (2002), no. 1, 169-186. MR 2003f:46108 - 9.
- J. M. Fell and R. S. Doran, Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles, Pure and Applied Mathematics 125 and 126, Academic Press, Boston, MA, 1988. MR 90c:46001, MR 90c:46002
- 10.
- A. Haefliger, Structures feuilletées et cohomologie à valeur dans un faiseau de groupoïdes, Comment. Math. Helv. 32 (1958), 248-329. MR 20:6702
- 11.
- K. Maclanahan, K-theory for partial crossed products by discrete groups, J. Funct. Anal. 130 (1995) 77-117. MR 96i:46083
- 12.
- A. Nica, On a groupoid construction for actions of certain inverse semigroups, Internat. J. Math. 5 (1994), 349-372. MR 95h:46086
- 13.
- A. L. T. Paterson, Groupoids, inverse semigroups, and their operator algebras, Progress in Mathematics 170, Birkhaüser Boston, 1999. MR 2001a:22003
- 14.
- J. C. Quigg and I. Raeburn, Characterizations of crossed products by partial actions, J. Operator Theory 37 (1997), No. 2, 311-340. MR 99a:46121
- 15.
- J. C. Quigg and N. Sieben,
 -actions of  -discrete groupoids and inverse semigroups, J. Austral. Math. Soc. Ser. A 66 (1999), 143-167. MR 2000k:46097 - 16.
- Jean Renault, A groupoid approach to
 -algebras, Lecture Notes in Math. 793, Springer-Verlag, Berlin, 1980. MR 82h:46075 - 17.
- N. Sieben,
 -crossed products by partial actions and actions of inverse semigroups, J. Austral. Math. Soc. Ser. A 63 (1997), 32-46. MR 2000b:46124
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Additional Information:
Fernando
Abadie
Affiliation:
Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400, Montevideo, Uruguay
Email:
fabadie@cmat.edu.uy
DOI:
10.1090/S0002-9939-03-07300-3
PII:
S 0002-9939(03)07300-3
Keywords:
Groupoids,
Fell bundles,
partial actions
Received by editor(s):
April 25, 2001
Received by editor(s) in revised form:
October 24, 2002
Posted:
November 7, 2003
Additional Notes:
This work was partially financied by Fapesp, Brazil, Processo No. 95/04097-9
Communicated by:
David R. Larson
Copyright of article:
Copyright
2003,
American Mathematical Society
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