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) |
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Pages (from-to) | 451-478 |
Number of pages | 28 |
Journal | Transformation Groups |
Volume | 21 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1 2016 |
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology