On the variety of lagrangian subalgebras, II

Sam Evens; Jiang-Hua Lu

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

On the variety of lagrangian subalgebras, I

Sam Evens, Jiang-Hua Lu (2001)

Annales scientifiques de l'École Normale Supérieure

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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 $π : X \to X / / G$ contains a dense orbit. If $G$ is connected and reductive, then the action has fixed points if $\dim X / / G \leq 3$ .

The minimal orbit in a simple Lie algebra and its associated maximal ideal

A. Joseph (1976)

Annales scientifiques de l'École Normale Supérieure

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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.

A convexity theorem for Poisson actions of compact Lie groups

Hermann Flaschka, Tudor Ratiu (1996)

Annales scientifiques de l'École Normale Supérieure

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