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Poisson Lie Groups, Quantum Duality Principle, and the Quantum Double
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The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual, and their Heisenberg double in a way which extends both the theory of coadjoint orbits and the classical Fourier transform. We also describe the twisted Heisenberg double which is relevant for the study of nontrivial deformations of the quantized universal enveloping algebras.
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Cited by 2 Pith papers
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Universal $T$-matrices for quantum Poincar\'e groups: contractions and quantum reference frames
A new quantum deformation of the centrally extended Poincaré algebra is introduced whose universal T-matrix contracts to the Galilei T-matrix for quantum reference frames and appears as a central extension of the spac...
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Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
Coreductivity and cosymmetry of a Lie bialgebra are defined and shown to characterize when the complementary dual homogeneous space is reductive or symmetric, with applications to κ-deformed Lorentzian spacetimes.
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