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.
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Communicated by N. Yu. Reshetikhin
Supported in part by a Soros Foundation Grant awarded by the American Physical Society
Unité Associée au C.N.R.S., URA 280
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Alekseev, A.Y., Malkin, A.Z. Symplectic structures associated to Lie-Poisson groups. Commun.Math. Phys. 162, 147–173 (1994). https://doi.org/10.1007/BF02105190
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DOI: https://doi.org/10.1007/BF02105190