ON ALGEBRAIC VOLUME DENSITY PROPERTY |
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Authors: | SH KALIMAN F KUTZSCHEBAUCH |
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Institution: | 1.Department of Mathematics,University of Miami,Coral Gables,USA;2.Mathematisches Institut,Universit?t Bern,Bern,Switzerland |
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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 complete 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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