Algebraic density property of homogeneous spaces

Details Algebraic density property of homogeneous spaces Algebraic density property of homogeneous spaces

2008-06-11

arxiv.org/abs/0806.1935v3

Mathematics

Algebraic Geometry

26 pages

Scientific paper

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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