Seminar Algebra and Geometry: Matthias Leuenberger (Universität Bern)

Lie Algebra generated by LNDs on surfaces {xy=p(z)}

For Cⁿ the Lie algebra generated by locally nilpotent derivations (LNDs) is equal to the Lie algebra of all divergence free algebraic vector fields. It is not known which other smooth affine varieties have this property. We will see an answer to this question for smooth surfaces given by xy=p(z): It turns out that here the Lie algebra generated by LNDs is a subalgebra of codimension deg(p)-2 inside the divergence free vector fields.

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