Symplectic structures associated to Lie-Poisson groups

  title={Symplectic structures associated to Lie-Poisson groups},
  author={A. Z. Malkin},
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. On leave of absence from LOMI, Fontanka 27, St.Petersburg, Russia. Unité Associée au C.N.R.S., URA 280. LPTHE, Paris-VI, Tour 16 1er étage, 4 place Jussieu, F… CONTINUE READING
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Semenov - Tian - Shansky , Poisson - Lie groups , quantum duality principle and the twisted quantum double

  • P. Štoviček Jurčo
  • Theor . Math . Phys . v .
  • 1992

Path integral quantization of the coadjoint orbits of the Virasoro group and 2 - D gravity

  • S. Shatashvili Alekseev
  • Nucl . Phys . B
  • 1990

Poisson - Lie groups , dressing transformations and Bruhat decompositions

  • A. Weinstein
  • J . Diff . Geom .
  • 1986

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