关于Lagrange子代数的簇
On the variety of Lagrangian subalgebras
摘要：
研究了半单李代数关于Killing型的虚部的Lagrange子代数。证明了拉格朗日子代数簇$\Lagr$具有自然Poisson结构$Π$ .我们确定了$\Lagr$的不可约分支，证明了每个不可约分支是广义旗簇上的光滑纤维丛，并且该纤维是De Concini-Procesi紧化的实点与紧齐性空间的乘积.本文研究了Poisson结构$Π$的一些性质，证明了它包含许多有趣的Poisson子流形.
英文摘要：
We study Lagrangian subalgebras of a semisimple Lie algebra with respect to the imaginary part of the Killing form. We show that the variety $\Lagr$ of Lagrangian subalgebras carries a natural Poisson structure $Π$. We determine the irreducible components of $\Lagr$, and we show that each irreducible component is a smooth fiber bundle over a generalized flag variety, and that the fiber is the product of the real points of a De Concini-Procesi compactification and a compact homogeneous space. We study some properties of the Poisson structure $Π$ and show that it contains many interesting Poisson submanifolds.
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