Measured quantum groupoids associated with matched pairs of locally compact groupoids

Jean-Michel Vallin[1]

  • [1] Administrative address: MAPMO UMR 6628 CNRS / Université d’Orléans, France Alternative address: IMJ - Paris Rive Gauche Bâtiment Sophie Germain - pièce 709 Case 7012 5 rue Thomas Mann F-75205 PARIS Cedex 13

Annales mathématiques Blaise Pascal (2014)

  • Volume: 21, Issue: 2, page 81-133
  • ISSN: 1259-1734

Abstract

top
Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.

How to cite

top

Vallin, Jean-Michel. "Measured quantum groupoids associated with matched pairs of locally compact groupoids." Annales mathématiques Blaise Pascal 21.2 (2014): 81-133. <http://eudml.org/doc/275562>.

@article{Vallin2014,
abstract = {Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.},
affiliation = {Administrative address: MAPMO UMR 6628 CNRS / Université d’Orléans, France Alternative address: IMJ - Paris Rive Gauche Bâtiment Sophie Germain - pièce 709 Case 7012 5 rue Thomas Mann F-75205 PARIS Cedex 13},
author = {Vallin, Jean-Michel},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Von Neumann algebras; measured quantum groupoids; matched pairs of groupoids; von Neumann algebras},
language = {eng},
month = {7},
number = {2},
pages = {81-133},
publisher = {Annales mathématiques Blaise Pascal},
title = {Measured quantum groupoids associated with matched pairs of locally compact groupoids},
url = {http://eudml.org/doc/275562},
volume = {21},
year = {2014},
}

TY - JOUR
AU - Vallin, Jean-Michel
TI - Measured quantum groupoids associated with matched pairs of locally compact groupoids
JO - Annales mathématiques Blaise Pascal
DA - 2014/7//
PB - Annales mathématiques Blaise Pascal
VL - 21
IS - 2
SP - 81
EP - 133
AB - Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.
LA - eng
KW - Von Neumann algebras; measured quantum groupoids; matched pairs of groupoids; von Neumann algebras
UR - http://eudml.org/doc/275562
ER -

References

top
  1. Nicolás Andruskiewitsch, Sonia Natale, Tensor categories attached to double groupoids, Adv. Math. 200 (2006), 539-583 Zbl1099.16016MR2200856
  2. Saad Baaj, Georges Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de C * -algèbres, Ann. Sci. École Norm. Sup. (4) 26 (1993), 425-488 Zbl0804.46078MR1235438
  3. Saad Baaj, Georges Skandalis, Stefaan Vaes, Non-semi-regular quantum groups coming from number theory, Comm. Math. Phys. 235 (2003), 139-167 Zbl1029.46113MR1969723
  4. Saad Baaj, Georges Skandalis, Stefaan Vaes, Measurable Kac cohomology for bicrossed products, Trans. Amer. Math. Soc. 357 (2005), 1497-1524 (electronic) Zbl1062.22009MR2115374
  5. A. Connes, On the spatial theory of von Neumann algebras, J. Funct. Anal. 35 (1980), 153-164 Zbl0443.46042MR561983
  6. Michel Enock, Measured quantum groupoids in action, Mém. Soc. Math. Fr. (N.S.) (2008) Zbl1189.58002MR2541012
  7. Michel Enock, The unitary implementation of a measured quantum groupoid action, Ann. Math. Blaise Pascal 17 (2010), 233-302 Zbl1235.46066MR2778919
  8. Michel Enock, Measured quantum groupoids with a central basis, J. Operator Theory 66 (2011), 3-58 Zbl1265.46106MR2806546
  9. Michel Enock, Jean-Marie Schwartz, Kac algebras and duality of locally compact groups, (1992), Springer-Verlag, Berlin Zbl0805.22003MR1215933
  10. Michel Enock, Jean-Michel Vallin, Inclusions of von Neumann algebras, and quantum groupoids, J. Funct. Anal. 172 (2000), 249-300 Zbl0974.46055MR1753177
  11. Claude Godbillon, Éléments de topologie algébrique, (1971), Hermann, Paris Zbl0907.55001MR301725
  12. C. Anantharaman-Delaroche et J. Renault., Amenable groupoids, 36 (2000), L’Enseignement Mathématique, Geneva Zbl0960.43003MR1799683
  13. Johan Kustermans, Stefaan Vaes, Locally compact quantum groups, Ann. Sci. École Norm. Sup. (4) 33 (2000), 837-934 Zbl1034.46508MR1832993
  14. F. Lesieur, tel.ccsd.cnrs.fr/documents/archives0/00/00/55/05 
  15. Franck Lesieur, Measured quantum groupoids, Mém. Soc. Math. Fr. (N.S.) (2007) Zbl1221.46003MR2474165
  16. A Ramsey, Topologies on measured groupoids, Journal of Functional Analysis (1982), 314-343 Zbl0519.22003MR665021
  17. Jean Renault, A groupoid approach to C * -algebras, 793 (1980), Springer, Berlin Zbl0433.46049MR584266
  18. Jean-Luc Sauvageot, Sur le produit tensoriel relatif d’espaces de Hilbert, J. Operator Theory 9 (1983), 237-252 Zbl0517.46050MR703809
  19. Şerban Strătilă, Modular theory in operator algebras, (1981), Editura Academiei-Abacus Press Wells England Zbl0504.46043MR696172
  20. Stefaan Vaes, The unitary implementation of a locally compact quantum group action, J. Funct. Anal. 180 (2001), 426-480 Zbl1011.46058MR1814995
  21. Stefaan Vaes, Groupes quantiques localement compacts, actions et extensions, (2004) 
  22. Stefaan Vaes, Leonid Vainerman, Extensions of locally compact quantum groups and the bicrossed product construction, Adv. Math. 175 (2003), 1-101 Zbl1034.46068MR1970242
  23. Jean-Michel Vallin, Bimodules de Hopf et poids opératoriels de Haar, J. Operator Theory 35 (1996), 39-65 Zbl0849.22002MR1389642
  24. Jean-Michel Vallin, Unitaire pseudo-multiplicatif associé à un groupoïde. Applications à la moyennabilité, J. Operator Theory 44 (2000), 347-368 Zbl0986.22002MR1794823
  25. Jean-Michel Vallin, Actions and coactions of finite quantum groupoids on von Neumann algebras, extensions of the matched pair procedure, J. Algebra 314 (2007), 789-816 Zbl1128.46026MR2344585
  26. Jean-Michel Vallin, Relative matched pairs of finite groups from depth two inclusions of von Neumann algebras to quantum groupoids, J. Funct. Anal. 254 (2008), 2040-2068 Zbl1146.46040MR2402083
  27. S. L. Woronowicz, From multiplicative unitaries to quantum groups, Internat. J. Math. 7 (1996), 127-149 Zbl0876.46044MR1369908

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.