Poisson Lie Groups, Quantum Duality Principle, and the Quantum Double

Details Poisson Lie Groups, Quantum Duality Principle, and the Quantum Double Poisson Lie Groups, Quantum Duality Principle, and the Quantum Double

1993-04-10

arxiv.org/abs/hep-th/9304042v1

Theor.Math.Phys. 93 (1992) 1292-1307; Teor.Mat.Fiz. 93N2 (1992) 302-329

Physics

High Energy Physics

High Energy Physics - Theory

31 pages

Scientific paper

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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