Groupes quantiques : techniques galoisiennes et d'intégration
Projet ANR BLAN07-3_183390
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.
T. Banica,
J. Bichon and
S. Curran, Quantum automorphisms of twisted group algebras and free hypergeometric laws,
Proc. Amer. Math. Soc., to appear.
T. Banica,
J. Bichon and S. Natale, Finite quantum groups and quantum permutation groups, arxiv:1104.1400.
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, Indiana Univ. Math. J. 59 (2010), 839-856.
T. Banica,
B. Collins,
and J.-M. Schlenker, On polynomial integrals over the orthogonal group, J. Combin. Theory Ser. A 118 (2011), 778-795.
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 and
S. Curran, Decomposition results for Gram matrix determinants, J. Math. Phys. 51 (2010), 1-14
T. Banica, S. Curran and R. Speicher, Classification results for easy quantum groups, Pacific J. Math. 247 (2010), 1-26.
T. Banica,
S. Curran and R. Speicher, De Finetti theorems for easy quantum groups, Ann. Probab. , to appear, arxiv:0907.3314.
T. Banica,
S. Curran and R. Speicher, Stochastic aspects of easy quantum groups,
Probab. Theory Related Fields 149 (2011), 435-462.
T. Banica and D. Goswami, Quantum isometries and noncommutative spheres, Comm. Math. Phys 298 (2010), 343-356.
T. Banica and
I. Nechita, Asymptotic eigenvalue distributions of block-transposed Wishart matrices, arxiv:1105.2556.
T. Banica and J.-M. Schlenker, Combinatorial aspects of orthogonal group integrals, Internat. J. Math., to appear.
T. Banica and
A. Skalski, Two-parameter families of quantum symmetry groups, J. Funct. Anal. 260 (2011), 3252-3282.
T. Banica and
A. Skalski, Quantum isometry groups of duals of free powers of cyclic groups, Int. Math. Res. Not., to appear.
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 60 (2010), 2137-2164.
J. Bichon, Algebraic quantum permutation groups, Asian-Eur. J. Math. 1 (2008), 1-13.
J. Bichon,
Hopf-Galois objects and cogroupoids, Pub. Mat. Uruguay, to appear.
J. Bichon
and C. Kassel, The lazy homology of a Hopf algebra, J. Algebra 323(2010), 2556-2590.
J. Bichon
and S. Natale, Hopf algebra deformations of binary polyhedral groups, Transform. Groups 16 (2011), 339-374.
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,
Hopf algebras and polynomial identities , Proc. Conf. "Quantum Groups and Quantum Topology", RIMS Kokyuroku 1714, 2010, 49-62
C. Kassel,
Generic Hopf Galois extensions, Proc. 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), vol. E41, 2011, 104-120.
P. Guillot and C. Kassel, Cohomology of invariant Drinfeld twists on group algebras, Int. Math. Res. Not. 2010 (2010), 1894-1939.
P. Guillot, C. Kassel and A. Masuoka, Twisting algebras using non-commutative torsors: explicit computations, Math. Z., to appear.
C. Kassel
and A. Masuoka, Flatness and freeness properties of the generic Hopf Galois extensions , Rev. Un. Mat. Argentina 51(2010), 79-94.
S. Vaes and N. Vander Vennet,
Poisson boundary of the discrete quantum group Au(F)^, Compositio Math. 146 (2010), 1073-105.