On complete generators of certain Lie algebras on Danielewski surfaces
Abstract
We study the Lie algebra of polynomial vector fields on a smooth Danielewski surface of the form [Formula: see text] with [Formula: see text]. We provide explicitly given generators to show that: (1) The Lie algebra of polynomial vector fields is generated by [Formula: see text] complete vector fields. (2) The Lie algebra of volume-preserving polynomial vector fields is generated by finitely many complete vector fields, whose number depends on the degree of the defining polynomial [Formula: see text]. (3) There exists a Lie sub-algebra generated by [Formula: see text] LNDs whose flows generate a group that acts infinitely transitively on the Danielewski surface. The latter result is also generalized to higher dimensions where [Formula: see text].
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Algebra and Geometry
Geometry and complex manifolds
Publication details
- Journal / source
- International Journal of Mathematics
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 37
- Issue
- 09
- Publication date
- 17 April 2026
- Language
- EN