Introduction 1 Poisson-Lie groups and Lie bialgebras 1.1 Poisson manifolds A Definitions B Functorial properties C Symplectic leaves 1.2 Poisson-Lie groups A Definitions B Poisson homogeneous spaces 1.3 Lie bialgebras A The Lie bialgebra of a Poisson-Lie group B Martintriples C Examples D Derivations 1.4 Duals and doubles A Duals of Lie bialgebras and Poisson-Lie groups B The classical double C Compact Poisson-Lie groups 1.5 Dressing actions and symplectic leaves A Poisson actions B Dressing transformations and symplectic leaves C Symplectic leaves in compact Poisson-Lie groups D Thetwsted ease 1.6 Deformation of Poisson structures and quantization A Deformations of Poisson algebras BWeylquantization C Quantization as deformation Bibliographical notes 2 Coboundary PoissoI-Lie groups and the classical Yang-Baxter equation 3 Solutions of the classical Yang-Baxterequation 4 Quasitriangular Hopf algebras 5 Representations and quasitensor categories 6 Quantization of Lie bialgebras 7 Quantized function algebras 8 Structure of QUE algebras:the universal R-matrix 9 Specializations of QUE algebras 10 Representations of QUE algebas the generic case 11 Representations of QUE algebas the root of unity case 12 Infinite-dimensionalquantum groups 13 Quantum harmonic analysis 14 Canonical bases 15 Quantum gruop invariants f knots and 3-manifolds 16 Quasi-Hopf algebras and the Knizhnik -Zamolodchikov equation
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