### 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 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 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 language | English (US) |
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Pages (from-to) | 551-576 |

Number of pages | 26 |

Journal | Transformation Groups |

Volume | 15 |

Issue number | 3 |

DOIs | |

State | Published - Apr 14 2010 |

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Donzelli, F., Dvorsky, A., & Kaliman, S. (2010). Algebraic density property of homogeneous spaces.

*Transformation Groups*,*15*(3), 551-576. https://doi.org/10.1007/s00031-010-9091-8