AI 中文总结
本文证明仿射空间上具常散度的多项式向量场的李代数是1.5生成的，且复仿射空间上所有多项式向量场的李代数由两个完全可积元素生成。
AI 中文摘要
若李代数的每个非零元素都可被补全为一个二元生成集，则称其为1.5生成的。本文证明，仿射空间上具有常散度的多项式向量场的李代数是1.5生成的；还证明，复仿射空间上所有多项式向量场的李代数由两个完全可积元素生成。
英文摘要
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.
