On the variety of lagrangian subalgebras, I
Sam Evens, Jiang-Hua Lu (2001)
Annales scientifiques de l'École Normale Supérieure
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Sam Evens, Jiang-Hua Lu (2001)
Annales scientifiques de l'École Normale Supérieure
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Martin Fankhauser (1995)
Annales de l'institut Fourier
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Let be a smooth, affine complex variety, which, considered as a complex manifold, has the singular -cohomology of a point. Suppose that is a complex algebraic group acting algebraically on . Our main results are the following: if is semi-simple, then the generic fiber of the quotient map contains a dense orbit. If is connected and reductive, then the action has fixed points if .
A. Joseph (1976)
Annales scientifiques de l'École Normale Supérieure
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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.
Hermann Flaschka, Tudor Ratiu (1996)
Annales scientifiques de l'École Normale Supérieure
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