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

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

1999-01-18

arxiv.org/abs/math/9901073v2

Mathematics

Quantum Algebra

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

Scientific paper

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.

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