
Journal of Lie Theory 33 (2023), No. 3, 919923 Copyright Heldermann Verlag 2023 Bracket Width of the Lie Algebra of Vector Fields on a Smooth Affine Curve Ievgen Makedonskyi Institut für Mathematik, FriedrichSchillerUniversität, Jena, Germany makedonskyi.e@gmail.com Andriy Regeta Institut für Mathematik, FriedrichSchillerUniversität, 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. [ Fulltextpdf (89 KB)] for subscribers only. 