Integrable Generators of Lie Algebras of Vector Fields on SL 2(C) and on xy= z2

Abstract

For the special linear group SL 2(C) and for the singular quadratic Danielewski surface xy= 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 xy= z2 . © 2023, The Author(s).