论文信息 - On Universal Fields of Fractions for Free Algebras

On Universal Fields of Fractions for Free Algebras

Abstract Let L be an arbitrary Lie algebra. Then by Cohn's Theorem its universal enveloping algebra can be embedded in a skew field D ( L ). We study this skew field in the case when L is a free Lie algebra and prove that in this case D ( L ) is isomorphic to the universal field of fractions for the free associative algebra U ( L ). We apply this theorem to obtain new results on free fields.

A. Lichtman

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