Algebraic (volume) density property for affine homogeneous spaces

Shulim Kaliman, Frank Kutzschebauch

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let X be a connected affine homogenous space of a linear algebraic group G over (Formula presented.). (1) If X is different from a line or a torus we show that the space of all algebraic vector fields on X coincides with the Lie algebra generated by complete algebraic vector fields on X. (2) Suppose that X has a G-invariant volume form (Formula presented.). We prove that the space of all divergence-free (with respect to (Formula presented.)) algebraic vector fields on X coincides with the Lie algebra generated by divergence-free complete algebraic vector fields on X (including the cases when X is a line or a torus). The proof of these results requires new criteria for algebraic (volume) density property based on so called module generating pairs.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalMathematische Annalen
DOIs
StateAccepted/In press - Aug 2 2016

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Affine Space
Homogeneous Space
Vector Field
Divergence-free
Torus
Lie Algebra
Volume formula
Linear Algebraic Groups
Line
Module
Invariant

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Algebraic (volume) density property for affine homogeneous spaces. / Kaliman, Shulim; Kutzschebauch, Frank.

In: Mathematische Annalen, 02.08.2016, p. 1-22.

Research output: Contribution to journalArticle

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