Rational Methods in the Theory of Lie Algebras

Introduction. The present note gives a development by rational methods of that part of the theory of Lie algebras (infinitesimal groups) which centers around the Lie-Engel theorems.' The main results are for the most part well known. The chief interest lies in the method, which consists of studying by elementary and direct means the relation between a Lie algebra and an enveloping associative algebra generated by it. The incidental machinery developed should be useful in rationalizing other parts of the theory. My interest in this subject was aroused by the lectures of Prof. Weyl. I am indebted also to Prof. Albert for collaborating with me in the early stages of this work.

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