A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups

Eugene Karolinsky

A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups

Quantum Algebra 2007-05-23 v2 Differential Geometry

Authors: Eugene Karolinsky

Abstract

Let $G$ be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous $G$ -spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence between Poisson homogeneous $G$ -spaces and Lagrangian subalgebras in the double $D(g)$ (here $g = Lie G$ ). A geometric interpretation of some of Poisson homogeneous $G$ -spaces is also proposed.

Keywords

poisson homogeneous spaces complex reductive groups poisson-lie groups sklyanin bracket lagrangian subalgebras drinfeld correspondence

Cite

@article{arxiv.math/9901073,
  title  = {A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups},
  author = {Eugene Karolinsky},
  journal= {arXiv preprint arXiv:math/9901073},
  year   = {2007}
}

Comments

LaTeX 2e, 9 pages, to be published in Banach Center Publications; minor changes (typos corrected)

A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups

Abstract

Keywords

Cite

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