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Poisson-Lie groups. The quantum duality principle and the twisted quantum double. (English. Russian original) Zbl 0834.22019
Theor. Math. Phys. 93, No. 2, 1292-1307 (1992); translation from Teor. Mat. Fiz. 93, No. 2, 302-329 (1992).
Summary: The quantum duality principle relates the quantum groups that arise on the quantization of Poisson-Lie dual groups and generalizes Fourier duality. Also considered are the theory of the Heisenberg double, which replaces the cotangent bundle for quantum groups, and its deformation (the twisted double).

22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory