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ON ALGEBRAIC VOLUME DENSITY PROPERTY

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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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Authors and Affiliations

  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    SH. KALIMAN

  2. Mathematisches Institut, Universität Bern, Sidlerstr. 5, CH-3012, Bern, Switzerland

    F. KUTZSCHEBAUCH

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  1. SH. KALIMAN
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  2. F. KUTZSCHEBAUCH
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Correspondence to SH. KALIMAN.

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2000 Mathematics Subject Classification. Primary: 32M05,14R20. Secondary: 14R10, 32M25.

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KALIMAN, S., KUTZSCHEBAUCH, F. ON ALGEBRAIC VOLUME DENSITY PROPERTY. Transformation Groups 21, 451–478 (2016). https://doi.org/10.1007/s00031-015-9360-7

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