科研之友
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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 fixed point free nondegenerate SL(2)-actions satisfying some mild additional assumption. Then we prove that the Lie algebra generated by completely integrable algebraic vector fields on X coincides with the space 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 a closed proper reductive subgroup of G.
- 出版日期2010-9
