摘要翻译:
设$X$是具有代数自同构群传递作用的仿射代数簇。假定$x$具有若干个非退化的不动点自由作用$sl_2$-满足一些温和的附加假设。然后我们证明了在$x$上由完全可积的代数向量场生成的李代数与所有代数向量场的集合重合。特别地,我们证明了除了一些例外情况之外,对于任何形式为$G/R$的齐次空间,这个事实都是成立的,其中$G$是线性代数群,$R$是它的适当约化子群。
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英文标题:
《Algebraic density property of homogeneous spaces》
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作者:
Fabrizio Donzelli, Alexander Dvorsky, and Shulim Kaliman
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最新提交年份:
2009
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Complex Variables 复变数
分类描述:Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数,自守群作用与形式,伪凸性,复几何,解析空间,解析束
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英文摘要:
Let $X$ be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that $X$ is equipped with several non-degenerate fixed point free $SL_2$-actions satisfying some mild additional assumption. Then we show that the Lie algebra generated by completely integrable algebraic vector fields on $X$ coincides with the set of all algebraic vector fields. In particular, we show that apart from a few exceptions this fact is true for any homogeneous space of form $G/R$ where $G$ is a linear algebraic group and $R$ is its proper reductive subgroup.
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PDF链接:
https://arxiv.org/pdf/0806.1935