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Algebraic Density Property of Homogeneous Spaces

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 non-degenerate SL_2-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 set 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 proper reductive subgroup of G.

Identiferoai:union.ndltd.org:UMIAMI/oai:scholarlyrepository.miami.edu:oa_dissertations-1208
Date25 April 2009
CreatorsDonzelli, Fabrizio
PublisherScholarly Repository
Source SetsUniversity of Miami
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceOpen Access Dissertations

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