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Integrable Generators of Polynomial Vector Fields for Complex Classical Lie Groups
Abstract
We consider in this paper complex Lie groups SLn(ℂ) for n≥ 2, SOn(ℂ) for n≥ 5, and Sp2n(ℂ) for n≥ 1. We show that for any such Lie group, the Lie algebra of polynomial vector fields can be generated by three ℂ-complete polynomial vector fields.
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BibTeX
@misc{jiang2026integrable,
title = {{Integrable Generators of Polynomial Vector Fields for Complex Classical Lie Groups}},
author = {Yiyang Jiang and Xudong Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02144},
eprint = {2609.02144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02144},
}
RIS
TY - UNPB
TI - Integrable Generators of Polynomial Vector Fields for Complex Classical Lie Groups
AU - Yiyang Jiang
AU - Xudong Chen
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02144
UR - https://arxiv.org/abs/2609.02144
AB - We consider in this paper complex Lie groups SL_n(ℂ) for n≥ 2, SO_n(ℂ) for n≥ 5, and Sp_2n(ℂ) for n≥ 1. We show that for any such Lie group, the Lie algebra of polynomial vector fields can be generated by three ℂ-complete polynomial vector fields.
ER -