ON ALGEBRAIC VOLUME DENSITY PROPERTY

Shulim Kaliman, F. KUTZSCHEBAUCH

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)451-478
Number of pages28
JournalTransformation Groups
Volume21
Issue number2
DOIs
StatePublished - Jun 1 2016

Fingerprint

Vector Field
Divergence
Linear Algebraic Groups
Algebraic Variety
Zero
Homogeneous Space
Lie Algebra
Subgroup
Closed
Invariant
Form

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 journalArticle

Kaliman, Shulim ; KUTZSCHEBAUCH, F. / ON ALGEBRAIC VOLUME DENSITY PROPERTY. In: Transformation Groups. 2016 ; Vol. 21, No. 2. pp. 451-478.
@article{88ac68f0f717448e82c75dd93d5c0821,
title = "ON ALGEBRAIC VOLUME DENSITY PROPERTY",
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.",
author = "Shulim Kaliman and F. KUTZSCHEBAUCH",
year = "2016",
month = "6",
day = "1",
doi = "10.1007/s00031-015-9360-7",
language = "English (US)",
volume = "21",
pages = "451--478",
journal = "Transformation Groups",
issn = "1083-4362",
publisher = "Birkhause Boston",
number = "2",

}

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 -