It is proved that any finite-dimensional Lie algebra over an algebraically closed field K of characteristic 0 can be embedded (realized) as a transitive Lie subalgebra of the Lie algebra of polynomial vector fields on the space Kⁿ. The same is also proved for arbitrary real Lie algebras and in some other cases.

中文翻译：

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有限维李代数的多项式实现

证明了，特征为0的代数闭合域K上的任何有限维李代数都可以作为多项式向量场的李代数在空间K ⁿ上的传递李代子嵌入（实现）。任意实李代数和其他情况也证明了这一点。