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.
| Identifer | oai:union.ndltd.org:UMIAMI/oai:scholarlyrepository.miami.edu:oa_dissertations-1208 |
| Date | 25 April 2009 |
| Creators | Donzelli, Fabrizio |
| Publisher | Scholarly Repository |
| Source Sets | University of Miami |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Open Access Dissertations |
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