Integrable Generators of Lie Algebras of Vector Fields on $$\textrm{SL}_2(\mathbb {C})$$ and on $$xy = z^2

For the special linear group $$\textrm{SL}_2(\mathbb {C})$$ SL 2 ( C ) and for the singular quadratic Danielewski surface $$x y = z^2$$ x y = z 2 we give explicitly a finite number of complete polynomial vector fields that generate the Lie algebra of all polynomial vector fields on them. Moreover, w...

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Bibliographic Details
Published in:The Journal of geometric analysis 2023-08, Vol.33 (8), Article 240
Main Author: Andrist, Rafael B.
Format: Article
Language:English
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Summary:For the special linear group $$\textrm{SL}_2(\mathbb {C})$$ SL 2 ( C ) and for the singular quadratic Danielewski surface $$x y = z^2$$ x y = z 2 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 $$x y = z^2$$ x y = z 2 .
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01294-x