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
ON ALGEBRAIC VOLUME DENSITY PROPERTY. / Kaliman, Shulim; KUTZSCHEBAUCH, F.
In: Transformation Groups, Vol. 21, No. 2, 01.06.2016, p. 451-478.Research output: Contribution to journal › Article
}
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 -