### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 451-478 |

Number of pages | 28 |

Journal | Transformation Groups |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2016 |

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### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Transformation Groups*,

*21*(2), 451-478. https://doi.org/10.1007/s00031-015-9360-7

**ON ALGEBRAIC VOLUME DENSITY PROPERTY.** / Kaliman, Shulim; KUTZSCHEBAUCH, F.

Research output: Contribution to journal › Article

*Transformation Groups*, vol. 21, no. 2, pp. 451-478. https://doi.org/10.1007/s00031-015-9360-7

}

TY - JOUR

T1 - ON ALGEBRAIC VOLUME DENSITY PROPERTY

AU - Kaliman, Shulim

AU - KUTZSCHEBAUCH, F.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84961644597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961644597&partnerID=8YFLogxK

U2 - 10.1007/s00031-015-9360-7

DO - 10.1007/s00031-015-9360-7

M3 - Article

AN - SCOPUS:84961644597

VL - 21

SP - 451

EP - 478

JO - Transformation Groups

JF - Transformation Groups

SN - 1083-4362

IS - 2

ER -