Kutzschebauch, Frank; Leuenberger, Matthias
(2016).
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The Lie algebra generated by locally nilpotent derivations on a Danielewski surface.
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Annali della Scuola normale superiore di Pisa - classe di scienze, 15, pp. 183-207.
Scuola normale superiore di Pisa

Text
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We give a full description of the Lie algebra generated by locally nilpotent derivations (short LNDs) on smooth Danielewski surfaces Dp given by xy=p(z) . In case deg(p)≥3 it turns out to be not the whole Lie algebra VF ω alg (Dp) of volume preserving algebraic vector fields, thus answering a question posed by Lind and the first author. Also we show algebraic volume density property (short AVDP) for a certain homology plane, a homogeneous space of the form SL₂ (C)/N , where N is the normalizer of the maximal torus and another related example.

## 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: |
Kutzschebauch, Frank and Leuenberger, Matthias |

## Subjects: |
500 Science > 510 Mathematics |

## ISSN: |
0391-173X |

## Publisher: |
Scuola normale superiore di Pisa |

## Language: |
English |

## Submitter: |
Olivier Bernard Mila |

## Date Deposited: |
13 Jul 2017 15:40 |

## Last Modified: |
13 Jul 2017 15:40 |

## ArXiv ID: |
1311.1075v2 |

## BORIS DOI: |
10.7892/boris.98611 |

## URI: |
https://boris.unibe.ch/id/eprint/98611 |