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

  • Ivan Beldiev
  • Gleb Pogudin
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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.

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Cite

BibTeXRIS
BibTeX
@misc{beldiev2026algebra,
  title = {{The Lie algebra of polynomial vector fields on the affine space with constant divergence is $1.5$-generated}},
  author = {Ivan Beldiev and Gleb Pogudin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.13798},
  eprint = {2608.13798},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.13798},
}
RIS
TY  - UNPB
TI  - The Lie algebra of polynomial vector fields on the affine space with constant divergence is $1.5$-generated
AU  - Ivan Beldiev
AU  - Gleb Pogudin
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.13798
UR  - https://arxiv.org/abs/2608.13798
AB  - 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.
ER  -