Groupes quantiques : techniques galoisiennes et d'intégration

Projet ANR BLAN07-3_183390


http://math.univ-bpclermont.fr/~bichon/Galoisinteng.html

Description. L'objectif du projet est de contribuer à la classification des groupes quantiques en étudiant deux sous-problèmes issus de la théorie des représentations : la classification des extensions de Hopf-Galois pour une algèbre de Hopf et la recherche de formules explicites pour la mesure de Haar. Le projet associe des chercheurs d'horizons divers : algèbre, algèbres d'opérateurs, probabilités libres.

Membres du projet.
Evénements.
Conférence ''Groupes quantiques'' à Clermont-Ferrand : semaine du 30 aout au 3 septembre 2010.
Evénements passés
14-16 mai 2009 : Workshop ``Groupes quantiques'' à l'institut de Mathématiques de Toulouse.
14-16 février 2008 : Journées ''Groupes quantiques'' à l'Institut de Recherche Mathématique Avancée, Strasbourg.


Publications.
  • E. Aljadeff and C. Kassel, Polynomial identities and noncommutative versal torsors, Adv. Math. 218 (2008), 1453-1495.
  • T. Banica, A note on free quantum groups, Ann. Math. Blaise Pascal 15 (2008), 135-146.
  • T. Banica, Cyclotomic expansion of exceptional spectral measures, Internat. J. Math. 20 (2009), 275-297.
  • T. Banica, The orthogonal Weingarten formula in compact form, Lett. Math. Phys. 91 (2010), 105-118.
  • T. Banica, The planar algebra of a fixed point subfactor, arxiv:0911.3073.
  • T. Banica, S.T. Belinschi, M. Capitaine and B. Collins, Free Bessel laws, Canad. J. Math, to appear, arXiv:0710.5931.
  • T. Banica and J. Bichon, Quantum groups acting on 4 points, J. Reine Angew. Math. 626 (2009), 74-114.
  • T. Banica and J. Bichon, Hopf images and inner faithful representations, Glasg. Math. J., to appear, arxiv:0807.3827.
  • T. Banica, J. Bichon and B. Collins, The hyperoctahedral quantum group, J. Ramanujan Math. Soc. 22 (2007), 345-384.
  • T. Banica, J. Bichon and S. Curran, Quantum automorphisms of twisted group algebras and free hypergeometric laws, arxiv:1002.3146.
  • T. Banica, J. Bichon and J.-M. Schlenker, Representations of quantum permutation algebras, J. Funct. Anal. 257 (2009), 2864-2910.
  • T. Banica, B. Collins and J.-M. Schlenker, On orthogonal matrices maximizing the 1-norm, arxiv:0901.2923.
  • T. Banica, B. Collins and P. Zinn-Justin, Spectral analysis of the free orthogonal matrix, Int. Math. Res. Not. 17 (2009), 3286-3309.
  • T. Banica, B. Collins, and J.-M. Schlenker, On polynomial integrals over the orthogonal group, arxiv:0910.1258.
  • T. Banica, S. Curran and R. Speicher, Classification results for easy quantum groups, Pacific J. Math., to appear, arxiv:0906.3890.
  • T. Banica, S. Curran and R. Speicher, De Finetti theorems for easy quantum groups, arxiv:0907.3314.
  • T. Banica, S. Curran and R. Speicher, Stochastic aspects of easy quantum groups, Probab. Theory Related Fields, to appear, arxiv:0909.0188.
  • T. Banica and D. Goswami, Quantum isometries and noncommutative spheres, Comm. Math. Phys, to appear, arxiv:0905.3814.
  • T. Banica and R. Speicher, Liberation of orthogonal Lie groups, Adv. Math 222 (2009), 1461-1501.
  • T. Banica and R. Vergnioux, Growth estimates for discrete quantum groups, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12 (2009), 321-340.
  • T. Banica and R. Vergnioux, Fusion rules for quantum reflection groups, J. Noncommut. Geom. 3 (2009), 327-359.
  • T. Banica and R. Vergnioux, Invariants of the half-liberated orthogonal group, Ann. Inst. Fourier, to appear, arxiv:0902.2719.
  • J. Bichon, Algebraic quantum permutation groups, Asian-Eur. J. Math. 1 (2008), 1-13.
  • J. Bichon and N. Andruskiewitsch, Examples of inner linear Hopf algebras, arXiv:0911.5585.
  • J. Bichon and C. Kassel, The lazy homology of a Hopf algebra, J. Algebra, to appear, arXiv:0807.1651.
  • J. Bichon and S. Natale, Hopf algebra deformations of binary polyhedral groups, arXiv:0907.1879.
  • B. Collins, J. Härtel and A. Thom, Homology of free quantum groups, C. R. Acad. Sci. Paris, Ser. I 347 (2009), 271-276.
  • C. Kassel, Generic Hopf Galois extensions, Proceedings of the Workshop on Quantum Groups and Noncommutative Geometry, M. Marcolli and D. Parashar (eds.), Max Planck Institut fur Mathematik, Bonn 2007, Vieweg Verlag (Max-Planck Series), to appear in 2009, arXiv:0809.0638.
  • P. Guillot and C. Kassel, Cohomology of invariant Drinfeld twists on group algebras, Int. Math. Res. Not., to appear, arXiv:0903.2807.
  • P. Guillot and C. Kassel, Twisting algebras using non-commutative torsors, arXiv:0911.5287.
  • C. Kassel and A. Masuoka, Flatness and freeness properties of the generic Hopf Galois extensions , Rev. Un. Mat. Argentina, to appear, arXiv:0911.3719.
  • S. Vaes and N. Vander Vennet, Poisson boundary of the discrete quantum group Au(F)^, Compositio Math., to appear, arXiv:0812.0804.