Resumen de Lie Algebra generated by locally nilpotent derivations on Danielewski surfaces

Frank Kutzschebauch, Matthias Leuenberger

• 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.