Integrable generators of Lie algebras of vector fields on SL₂(ℂ) and on xy = z²

2022/08/30 by Rafael B. Andrist, Andrist, Rafael B.
Mathematics · #14R10 #32E30 #32M17 #32M25 #32Q56 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2208.14434

openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the special linear group SL₂(ℂ) and for the singular quadratic Danielewski surface x y = z² we give explicitly a finite number of complete polynomial vector fields that generate the Lie algebra of all polynomial vector fields on them. Moreover, we give three unipotent one-parameter subgroups that generate a subgroup of algebraic automorphisms acting infinitely transitively on x y = z².

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