Algebraic density property of homogeneous spaces

F. Donzelli, A. Dvorsky, S. Kaliman

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Let X be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that X is equipped with several fixed point free nondegenerate SL2-actions satisfying some mild additional assumption. Then we prove that the Lie algebra generated by completely integrable algebraic vector fields on X coincides with the space of all algebraic vector fields. In particular, we show that apart from a few exceptions this fact is true for any homogeneous space of form G/R where G is a linear algebraic group and R is a closed proper reductive subgroup of G.

Original languageEnglish (US)
Pages (from-to)551-576
Number of pages26
JournalTransformation Groups
Volume15
Issue number3
DOIs
StatePublished - Apr 14 2010

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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