ON ALGEBRAIC VOLUME DENSITY PROPERTY

Shulim Kaliman, F. KUTZSCHEBAUCH

Research output: Contribution to journalArticle

7 Scopus citations

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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