### Abstract

Let X be a connected affine homogenous space of a linear algebraic group G over (Formula presented.). (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 (Formula presented.). We prove that the space of all divergence-free (with respect to (Formula presented.)) 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) |
---|---|

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Mathematische Annalen |

DOIs | |

State | Accepted/In press - Aug 2 2016 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Algebraic (volume) density property for affine homogeneous spaces'. Together they form a unique fingerprint.

## Cite this

*Mathematische Annalen*, 1-22. https://doi.org/10.1007/s00208-016-1451-9