Integrable generators of Lie algebras of vector fields on ${\rm SL}_2({\mathbb C})$ and on $xy = z^2$

Andrist, Rafael Benedikt (author)

For the special linear group ${\rm SL}_2({\mathbb C})$ and for the singular quadratic Danielewski surface $xy = z^2$ 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 $xy = z^2$.

• Language: English
• Keywords: density property, finitely generated Lie algebra, completely integrable vector fields, Andersen–Lempert theory, infinitely transitive
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 18 str.
• Numbering: Vol. 33, iss. 8, art. 240
• PID: 20.500.12556/RUL-153556
• UDC: 517.5
• ISSN on article: 1050-6926
• DOI: 10.1007/s12220-023-01294-x
• COBISS.SI-ID: 179950595
• Publication date in RUL: 15.01.2024

Record is a part of a journal

• Title: The journal of geometric analysis
• Shortened title: J. geom. anal.
• Publisher: Springer Nature, Mathematica Josephina, Inc.
• ISSN: 1050-6926
• COBISS.SI-ID: 30685696

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Projects

• Funder: Other - Other funder or multiple funders
• Funding programme: American University of Beirut, University Research Board
• Project number: 104107

• Funder: ARRS - Slovenian Research Agency
• Project number: N1-0237
• Name: Holomorfne parcialne diferencialne relacije