Kaliman, Shulim; Kutzschebauch, Frank
(2017).
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Algebraic (volume) density property for affine homogeneous spaces.
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Mathematische Annalen, 367(3-4), pp. 1311-1332.
Springer
10.1007/s00208-016-1451-9

Text
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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.

## Item Type: |
Journal Article (Original Article) |
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## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |

## UniBE Contributor: |
Kaliman, Shulim and Kutzschebauch, Frank |

## Subjects: |
500 Science > 510 Mathematics |

## ISSN: |
0025-5831 |

## Publisher: |
Springer |

## Language: |
English |

## Submitter: |
Olivier Bernard Mila |

## Date Deposited: |
17 Apr 2018 15:28 |

## Last Modified: |
27 Oct 2019 12:22 |

## Publisher DOI: |
10.1007/s00208-016-1451-9 |

## BORIS DOI: |
10.7892/boris.109157 |

## URI: |
https://boris.unibe.ch/id/eprint/109157 |