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arXiv · 1201.4769

On algebraic volume density property

Shulim Kaliman·Frank Kutzschebauch
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Abstract

A smooth affine algebraic variety $X$ equipped with an algebraic volume form $ω$ has the algebraic volume density property (AVDP) if the Lie algebra generated by completely integrable algebraic vector fields of $ω$-divergence zero coincides with the space of all algebraic vector fields of $ω$-divergence zero. We develop an effective criterion of verifying whether a given $X$ has AVDP. As an application of this method we establish AVDP for any homogeneous space $X=G/R$ that admits a $G$-invariant algebraic volume form where $G$ is a linear algebraic group and $R$ is a closed reductive subgroup of $G$.

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Shulim Kaliman, Frank Kutzschebauch. 2014-02-06. On algebraic volume density property. https://arxiv.org/abs/1201.4769

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