Work

The Lie algebra of polynomial vector fields on the affine space with constant divergence is $1.5$-generated

Year: 2026

Type: preprint

Abstract: A Lie algebra is said to be $1.5$-generated if every nonzero element can be completed to a two-element generating set. We prove that the Lie algebra of polynomial vector fields with constant divergence on the affine space is $1.5$-generated. We also show that the Lie algebra of all polynomial vector fields on the complex affine space is generated by two completely integrable elements.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.13798

Authors: Beldiev, Ivan, Pogudin, Gleb

Institutions: National Research University Higher School of Economics, Centre National de la Recherche Scientifique, Laboratoire d'Informatique de l'École Polytechnique, École Polytechnique, Institut Polytechnique de Paris

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Numeric-symbolic resolution of differential equations, Theory and practice of differential elimination

OpenAlex ID: W7203606152

Cites:

Cited by:

Related to: 10