Algebraic (volume) density property for affine homogeneous spaces

Shulim Kaliman, Frank Kutzschebauch

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let X be a connected affine homogenous space of a linear algebraic group G over C. (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 ω. We prove that the space of all divergence-free (with respect to ω) 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)1311-1332
Number of pages22
JournalMathematische Annalen
Volume367
Issue number3-4
DOIs
StatePublished - Apr 1 2017

ASJC Scopus subject areas

  • Mathematics(all)

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