Bracket width of the Lie algebra of vector fields on a smooth affine curve

2022/10/26 by Makedonskyi, Ievgen, Regeta, Andriy
#Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2210.14787

Abstract

We prove that the bracket width of the simple Lie algebra of vector fields \rmVec(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 \rmVec(C) is at most two and if moreover C has a unique place at infinity, the bracket width of \rmVec(C) is exactly two. We also show that in case C is rational, the width of \rmVec(C) equals one.

Related

• Bracket width of simple Lie algebras
• Bracket width of current Lie algebras
• Lie algebras of vector fields on smooth affine varieties
• The Lie bracket of undirected curves on a surface
• Minimal intersection of curves on surfaces