Project GALOISINT

Quantum groups: Galois and integration techniques

Project ANR BLAN07-3_183390

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

Description of the project. The aim of the project is to contribute to the classification of quantum groups by studying two subproblems arising in representation theory: the classification of Hopf-Galois extensions of a Hopf algebra and the search of explicit formulae for the Haar measure. The project associates mathematicians having different backgroud and expertise: algebra, operator algebras, free probability.

Members of the project.

Thomas Aubriot . ATER (2008), Institut de Mathématiques de Bourgogne (UMR 5584), Université de Bourgogne (Dijon).
Teodor Banica. Professeur, Institut de Mathématiques de Toulouse (UMR 5219), Université Paul Sabatier (Toulouse III).
Julien Bichon . Professeur, Laboratoire de Mathématiques (UMR 6620), Université Blaise Pascal (Clermont-Ferrand II).
Benoît Collins. Chargé de Recherche CNRS, Institut Camille Jordan (UMR 5208), Université Claude Bernard (Lyon I)
Christian Kassel, Directeur de recherche CNRS, Institut de Recherche Mathématique Avancée (UMR 7501), Université Louis Pasteur (Strasbourg I).
Nikolas Vander Vennet, Post-doctorant (2008-2009), Laboratoire de Mathématiques (UMR 6620), Université Blaise Pascal (Clermont-Ferrand II).

Events.
Conference ''Quantum Groups'' at Clermont-Ferrand : august 30 - september 3, 2010.
Past events.
14-16 may 2009 : ``Quantum Groups Workshop'' at the Mathematics Institute of Toulouse .
14-16 february 2008: ''Quantum groups days'' at Strasbourg, Institut de Recherche Mathématique Avancée.

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.