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Communications in Algebra Volume 44, 2016 - Issue 1
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Original Articles

On Noncommutative Bases of Free Modules of Derivations over Polynomial Rings

Ievgen Makedonskyi Faculty of Mechanics and Mathematics, Kiev Taras Shevchenko University, Kiev, UkraineCorrespondence[email protected]
Pages 11-25 | Received 07 Sep 2011, Published online: 19 Oct 2015
 
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Abstract

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.

2010 Mathematics Subject Classification:

ACKNOWLEDGMENT

The author is grateful to Professor A. P. Petravchuk for suggesting the problem and for constant attention to this work.

Notes

Communicated by I. Shestakov.

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