ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 17, 20, 53 Karolinsky, Eugene, Kharkov State University, Ukraine A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups 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 Gspaces 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.