The Lie algebra generated by locally nilpotent derivations on a Danielewski surface

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

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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)

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

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