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On Noncommutative Bases of Free Modules of Derivations over Polynomial Rings

Let 𝕂 be an algebraically closed field of characteristic zero and W n be the Lie algebra of all 𝕂-derivations of the polynomial ring R in n variables over 𝕂. It is proved that every Lie algebra of dimension n over 𝕂 can be isomorphically embedded in W n in such a way that any basis of its image (over 𝕂) is a basis of the free module W n over R.