Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups

Communications in Mathematical Physics

Volumn 262, Issue 3, 2006, Pages 703-728

  Bichon, Julien ^a   De Rijdt, An ^b   Vaes, Stefaan ^b,c  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b UNIVERSITY OF LEUVEN   (Belgium)

^c INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31744446632     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1442-2     Document Type: Article

References (33)

1. Baaj, S., Skandalis, O.: Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres. Ann. Scient. Ec. Norm. Sup. 26, 425-488 (1993)
2. Banica, T.: Théorie des représentations du groupe quantique compact libre O(n). C. R. Acad. Sci. Paris Sér. I Math. 322, 241-244 (1996)
3. Banica, T.: Le groupe quantique compact libre U(n). Commun. Math. Phys. 190, 143-172 (1997)
4. Banica, T.: Quantum automorphism groups of homogeneous graphs. J. Funct. Anal. 224, 243-280 (2005)
5. Banica, T.: Quantum automorphism groups of small metric spaces. Pac. J. Math. 219, 27-52 (2005)
6. Bichon, J.: Galois extension for a compact quantum group. http://arxiv.org/list/math.QA/9902031, 1999
7. Bichon, J.: The representation category of the quantum group of a non-degenerate bilinear form. Comm. Algebra 31, 4831-4851 (2003)
8. Bichon, J.: Corepresentation theory of universal cosovereign Hopf algebras, http://arxiv.org/list/math.QA/0211059, 2002
9. Bichon, J.: Quantum automorphism groups of finite graphs. Proc. Amer. Math Soc. 131, 665-673 (2003)
10. Boca, F.: Ergodic actions of compact matrix pseudogroups on C*-algebras. In: Recent advances in operator algebras (Orléans, 1992). Astérisque 232, 93-109 (1995)
11. Bruguières, A.: Dualité tannakienne pour les quasi-groupoïdes quantiques. Comm. Algebra 25, 737-767 (1997)
12. Carter, J.S., Flath, D.E., Saito, M.: The classical and quantum 6 j-symbols. Mathematical Notes 43, Princeton, NJ: Princeton University Press, 1995
13. Doplicher, S., Longo, R., Roberts, J.E., Zsidó, L.: A remark on quantum group actions and nuclearity. Rev. Math. Phys. 14, 787-796 (2002)
14. Drinfel'd, V.G.: Quantum groups. In: Proceedings of the International Congress of Mathematicians, Providence, RI: Amer. Math. Soc., 1987, pp. 798-820
15. Etingof, P., Gelaki, S.: On cotriangular Hopf algebras. Amer. J. Math. 123, 699-713 (2001)
16. Høegh-Krohn, R., Landstad, M.B., Størmer, E.: Compact ergodic groups of automorphisms. Ann. of Math. (2) 114, 75-86 (1981)
17. Jimbo, M.: A q-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys. 10, 63-69 (1985)
18. Landstad, M.: Simplicity of crossed products from ergodic actions of compact matrix pseudogroups. In: Recent advances in operator algebras (Orléans, 1992). Astérisque 232, 111-114 (1995)
19. Landstad, M.: Ergodic actions of nonabelian compact groups. In: Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988), Cambridge: Cambridge Univ. Press, 1992, pp. 365-388
20. MacLane, S.: Categories for the working mathematician. Graduate Texts in Mathematics 5, Berlin-New York: Springer-Verlag, 1971
21. Rosso, M.: Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif. Duke Math. J. 61, 11-40 (1990)
22. Schauenburg, P.: Hopf bi-Galois extensions. Comm. Algebra 24, 3797-3825 (1996)
23. Tomatsu, R.: Compact quantum ergodic systems. http://arxiv.org/list/math. OA/0412012, 2004
24. Ulbrich, K.-H.: Galois extensions as functors of comodules. Manuscripta Math. 59, 391-397 (1987)
25. Van Daele. A., Wang, S.: Universal quantum groups. Internat. J. Math. 7, 255-263 (1996)
26. Wang, S.: Ergodic actions of universal quantum groups on operator algebras. Commun. Math. Phys. 203, 481-498 (1999)
27. Wassermann, A.: Ergodic actions of compact groups on operator algebras. I. General theory. Ann. of Math. (2) 130, 273-319 (1989)
28. Wassermann, A.: Ergodic actions of compact groups on operator algebras. II. Classification of full multiplicity ergodic actions. Canad. J. Math. 40, 1482-1527 (1988)
29. Wassermann, A.: Ergodic actions of compact groups on operator algebras. III. Classification for SU(2). Invent. Math. 93, 309-354 (1988)
30. Woronowicz, S.L.: Compact quantum groups. In: Symétries quantiques (Les Houches, 1995), Amsterdam: North-Holland, 1998, pp. 845-884
31. Woronowicz, S.L.: Twisted SU(2) group. An example of a non-commutative differential calculus. Publ. Res. Inst. Math. Sci. 23, 117-181 (1987)
32. Woronowicz, S.L.: Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups. Invent. Math. 93, 35-76 (1988)
33. Yamagami, S.: Fiber functors on Temperley-Lieb categories, http://arxiv.org/list/math.QA/0405517, 2004