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The center of the quotient division ring of the universal envelope of a Lie algebra

Author: Alfons I. Ooms
Journal: Proc. Amer. Math. Soc. 87 (1983), 394-396
MSC: Primary 17B35; Secondary 16A08
MathSciNet review: 684625
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Abstract: Let $ L$ be a finite dimensional Lie algebra over a field $ k$ of characteristic zero, $ D(L)$ the quotient division ring of $ U(L)$. We compare the center $ Z(D(L))$ with $ Z(D(H))$ where $ H$ is an ideal of $ L$ of codimension one.

References [Enhancements On Off] (What's this?)

  • [1] Pierre Bernat, Sur le corps enveloppant d’une algèbre de Lie résoluble, Bull. Soc. Math. France Mém. 7 (1966), 175 (French). MR 0230774
  • [2] J. Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents. II, Bull. Soc. Math. France 85 (1957), 325–388 (French). MR 0095426
  • [3] Jacques Dixmier, Algèbres enveloppantes, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). Cahiers Scientifiques, Fasc. XXXVII. MR 0498737

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Keywords: Finite dimensional Lie algebra, universal enveloping algebra, quotient division ring
Article copyright: © Copyright 1983 American Mathematical Society

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