Symplectic structures associated to Lie-Poisson groups |
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| Authors: | A Yu Alekseev A Z Malkin |
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| Institution: | (1) Laboratoire de Physique Théorique et Hautes Énergies, Paris, France;(2) Present address: Institute of Theoretical Physics, Uppsala University, Box 803, S-75108 Uppsala, Sweden;(3) LOMI, Fontanka 27, St. Petersburg, Russia;(4) Present address: St. Petersburg University, St. Petersburg, Russia;(5) LPTHE, Paris-VI, Tour 16-ler étage, 4 place Jussieu, F-75252 Paris Cedex 05, France |
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| Abstract: | The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified, and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.Supported in part by a Soros Foundation Grant awarded by the American Physical SocietyUnité Associée au C.N.R.S., URA 280 |
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