Displaying similar documents to “On the variety of lagrangian subalgebras, II”

Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser (1995)

Annales de l'institut Fourier

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Let X be a smooth, affine complex variety, which, considered as a complex manifold, has the singular ℤ -cohomology of a point. Suppose that G is a complex algebraic group acting algebraically on X . Our main results are the following: if G is semi-simple, then the generic fiber of the quotient map π : X → X / / G contains a dense orbit. If G is connected and reductive, then the action has fixed points if dim X / / G ≤ 3 .

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

Eugene Karolinsky (2000)

Banach Center Publications

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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 D𝖌 (here 𝖌 = Lie G). A geometric interpretation of some Poisson homogeneous G-spaces is also proposed.