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.
1
Institut für Mathematik, Friedrich-Schiller-Universität, Jena, Germany
Ievgen Makedonskyi; Andriy Regeta. Bracket Width of the Lie Algebra of Vector Fields on a Smooth Affine Curve. Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 919-923. http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a11/
@article{JOLT_2023_33_3_a11,
author = {Ievgen Makedonskyi and Andriy Regeta},
title = {Bracket {Width} of the {Lie} {Algebra} of {Vector} {Fields} on a {Smooth} {Affine} {Curve}},
journal = {Journal of Lie Theory},
pages = {919--923},
year = {2023},
volume = {33},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a11/}
}
TY - JOUR
AU - Ievgen Makedonskyi
AU - Andriy Regeta
TI - Bracket Width of the Lie Algebra of Vector Fields on a Smooth Affine Curve
JO - Journal of Lie Theory
PY - 2023
SP - 919
EP - 923
VL - 33
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a11/
ID - JOLT_2023_33_3_a11
ER -
%0 Journal Article
%A Ievgen Makedonskyi
%A Andriy Regeta
%T Bracket Width of the Lie Algebra of Vector Fields on a Smooth Affine Curve
%J Journal of Lie Theory
%D 2023
%P 919-923
%V 33
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a11/
%F JOLT_2023_33_3_a11
