## 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 language | English (US) |
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Pages (from-to) | 1311-1332 |

Number of pages | 22 |

Journal | Mathematische Annalen |

Volume | 367 |

Issue number | 3-4 |

DOIs | |

State | Published - Apr 1 2017 |

## ASJC Scopus subject areas

- Mathematics(all)