Quantum groups acting on 4 points

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 626, 2009, Pages 75-114

  Banica, Teodor ^a,b   Bichon, Julien ^a,c  

^a Université Paul Sabatier Toulouse III ^*

^b UNIVERSITÉ PAUL SABATIER   (France)

^c UNIVERSITÉ CLERMONT AUVERGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58449134871     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/CRELLE.2009.003     Document Type: Article

References (45)

1. V.I. Arnold, S. M. Gusein-Zade and A. N. Varchenko, Singularities of differentiable maps, Birkhäuser, 1985.
2. T. Banica, Symmetries of a generic coaction, Math. Ann. 314 (1999), 763-780.
3. T. Banica, Subfactors associated to compact Kac algebras, Integr. Equ. Oper. Th. 39 (2001), 1-14.
4. T. Banica, Quantum automorphism groups of homogeneous graphs, J. Funct. Anal, 224 (2005), 243-280.
5. T. Banica and J. Bichon, Free product formulae for quantum permutation groups, J. Inst. Math. Jussieu 6 (2007), 381-414.
6. T. Banica and J. Bichon, Quantum, automorphism, groups of vertex-transitive graphs of order g 11, J. Alg. Combin. 26 (2007), 83-105.
7. T. Banica, J. Bichon and G. Chenevier, Graphs having no quantum symmetry, Ann. Inst. Fourier 57 (2007), 955-971.
8. T. Banica, J. Bichon and B. Collins, The hyperoctahedral quantum group, J. Raman. Math. Soc. 22 (2007), 345-384.
9. T. Banica and D. Bisch, Spectral measures of small index principal graphs, Comm. Math. Phys. 269 (2007), 259-281.
10. T. Banica and B. Collins, Integration over quantum permutation groups, J. Funct. Anal. 242 (2007), 641-657.
11. T. Banica and B. Collins, Integration over the Pauli quantum group, J. Geom, Phys., to appear.
12. T. Banica and S. Moroianu, On the structure of quantum permutation groups, Proc. Amer. Math. Soc. 135 (2007), 21-29.
13. J. Bichon, Quelques nouvelles déformations du groupe symétrique, C. R. Acad. Sci. Paris 330 (2000), 761-764.
14. J. Bichon, Quantum automorphism groups of finite graphs, Proc. Amer. Math, Soc. 131 (2003), 665-673.
15. J. Bichon, Free wreath product by the quantum permutation group, AIg. Rep. Th. 7 (2004), 343-362.
16. A. Davydov, Galois algebras and monoidal functors between categories of representations of finite groups, J. Algebra 244 (2001), 273-301.
17. J. Dixon and B. Mortimer, Permutation groups, Grad. Texts Math, 163, Springer-Verlag, 1996.
18. Y. Doi, Braided bialgebras and quadratic algebras, Coram. Algebra 21 (.1993), 1731-1749.
19. V. Drinfeld, Quantum groups, Proc. ICM Berkeley (1986), 798-820.
20. M. Enock and L. Vainerman, Deformation of a Kac algebra by an abelian subgroup, Comm. Math. Phys. 178 (1996), 571-596.
21. P. Etingofand S. Gelaki, Some properties of finite-dimensional semisimple Hopf algebras, Math. Res. Lett. 5 (1998), 191-197.
22. P. Etingof and S. Gelaki, The representation theory of cotriangular semisimple Hopf algebras, Internat. Math. Res. Notices 7 (1999), 387-394.
23. P. Etingof zná S. Gelaki, The classification of triangular semisimple and cosemisimple Hopf algebras over an algebraically closed field, Internat. Math, Res. Notices 5 (2000), 223-234.
24. D. Evans and Y. Kawahigashi, Quantum, symmetries on operator algebras, Oxford University Press, 1998.
25. V. F. R. Jones, The annular structure of subfactors, Monogr. Enseign. Math. 38 (2001), 401-463.
26. A. Klimyk and K. Schmüdgen, Quantum groups and their representations, Texts and Monographs in Physics, Springer-Verlag, Berlin 1997.
27. S. Majid and R. Oeckl, Twisting of quantum differentials and the Planck scale Hopf algebra, Comm. Math. Phys. 205 (1999), 617-655.
28. Y. Manin, Quantum groups and noncommutative geometry, Publ. CRM 1561, Univ. de Montréal, 1988.
29. V. A. Marchenko and L. A. Pastur, Distribution of eigenvalues in certain sets of random matrices, Mat. Sb. 72 (1967), 507-536.
30. A. Masuoka, Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension, Contemp. Math. 267 (2000), 195-214.
31. J. McKay, Graphs, singularities and finite groups, Proc. Symp. Pure Math. 37 (1980), 183-186.
32. W. D. Nichols and M. B. Zoeller, A Hopf algebra freeness theorem, Amer. J. Math. 111 (1989), 381-385.
33. 0-rings and twisting of finite-dimensional semisimple Hopf algebras, Comm. Algebra 26 (1998), 321-342.
34. P. Podles, Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups, Comm. Math. Phys. 170 (1995), 1-20.
35. M. Rosso, Algebres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul, différentiel non-commutatif, Duke Math, J. 61 (1990), 11-40.
36. P. Schauenburg, Hopf bigalois extensions, Comm. Algebra 24 (1996), 3797-3825.
37. S. Suzuki, A family of braided cosemisimple Hopf algebras of finite dimension, Tsukuba J. Math. 22 (1998), 1-29.
38. L. Vainerman, 2-cocycles and twisting of Kac algebras, Comm. Math. Phys. 191 (1998), 697-721.
39. D. V. Vokulescu, K. J. Dykema and A. Nica, Free random variables, CRM Monogr. Ser. 1, AMS, 1992.
40. S. Wang, Free products of compact quantum, groups, Comm. Math. Phys. 167 (1995), 671-692.
41. S. Wang, Quantum symmetry groups of finite spaces, Comm. Math. Phys. 195 (1998), 195-211.
42. S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665.
43. S.L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Comm. Math, Phys. 122 (1989), 125-170.
44. S. L. Woronowicz, Compact quantum groups, in: Symétries quantiques (Les Houches 1995), North Holland, Amsterdam (1998), 845-884.
45. S. Zakrzewski, Matrix pseudogroups associated with anti-commutative plane, Lett. Math. Phys. 21 (1991), 309-321.