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On Lie algebras with primitive envelopes, supplements

Author: Alfons I. Ooms
Journal: Proc. Amer. Math. Soc. 58 (1976), 67-72
MSC: Primary 17B35
MathSciNet review: 0430007
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Abstract: Let $ L$ be a finite dimensional Lie algebra over a field $ k$ of characteristic zero, $ U(L)$ its universal enveloping algebra and $ Z(D(L))$ the center of the division ring of quotients of $ U(L)$. A number of conditions on $ L$ are each shown to be equivalent with the primitive of $ U(L)$. Also, a formula is given for the transcendency degree of $ Z(D(L))$ over $ k$.

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Keywords: Finite dimensional Lie algebra, universal enveloping algebra, primitive algebra, division ring of quotients
Article copyright: © Copyright 1976 American Mathematical Society

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