Lie Algebra generated by locally nilpotent derivations on Danielewski surfaces

• Frank Kutzschebauch ^[1] ; Matthias Leuenberger ^[1]
  1. [1] University of Bern

     University of Bern

     Bern/Berne/Berna, Suiza

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 183-207
• Idioma: inglés
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• Resumen

  • We give a full description of the Lie algebra generated by locally nilpotent derivations (shortly LNDs) on smooth Danielewski surfaces D p given by x y = p(z). In case deg( p) 3 it turns out that it is not equal to the whole Lie algebra VF! ( D p ) of volume-preserving algebraic vector fields, thus answering a question posed by Lind and the first author. We also show an algebraic volume density property (shortly AVDP) for a certain homology plane (a homogeneous space of the form S L 2 (C)/N , where N is the normalizer of the maximal torus) and a related example.