Journal of Lie Theory 33 (2023), No. 3, 919--923
Copyright Heldermann Verlag 2023
Bracket Width of the Lie Algebra of Vector Fields on a Smooth Affine Curve
Ievgen Makedonskyi
Institut für Mathematik, Friedrich-Schiller-Universität, Jena, Germany
makedonskyi.e@gmail.com
Andriy Regeta
Institut für Mathematik, Friedrich-Schiller-Universität, Jena, Germany
andriyregeta@gmail.com
We prove that the bracket width of the simple Lie algebra of vector fields Vec(C) of a smooth irreducible affine curve C with a trivial tangent sheaf is at most three. In addition, if C is a plane curve, the bracket width of Vec(C) is at most two and if moreover C has a unique place at infinity, the bracket width of Vec(C) is exactly two. We also show that in case C is rational, the width of Vec(C) equals one.
Keywords: Bracket width, Lie algebra of vector fields, smooth affine curves.
MSC: 14H50, 14H52, 17B66.
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