Journal of Lie Theory

no. 3
Bracket Width of the Lie Algebra of Vector Fields on a Smooth Affine Curve
Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 919-923
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.
DOI: 10.5802/jolt.1312
Classification: 14H50, 14H52, 17B66
Keywords: Bracket width, Lie algebra of vector fields, smooth affine curves 
@article{JOLT_2023_33_3_a11,
     author = {I. Makedonskyi and A. 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},
     doi = {10.5802/jolt.1312},
     zbl = {1533.14023},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1312/}
}
TY  - JOUR
AU  - I. Makedonskyi
AU  - A. 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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1312/
DO  - 10.5802/jolt.1312
ID  - JOLT_2023_33_3_a11
ER  - 
%0 Journal Article
%A I. Makedonskyi
%A A. 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 https://jolt.centre-mersenne.org/articles/10.5802/jolt.1312/
%R 10.5802/jolt.1312
%F JOLT_2023_33_3_a11
I. Makedonskyi; A. Regeta. Bracket Width of the Lie Algebra of Vector Fields on a Smooth Affine Curve. Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 919-923. doi: 10.5802/jolt.1312

Cited by Sources: