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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0430007-6
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$.


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

  • [1] A. Borel, Linear algebraic groups, Benjamin, New York, 1969. MR 40 #4273. MR 0251042 (40:4273)
  • [2] W. Borho, P. Gabriel and R. Rentschier, Primideale in Einhüllenden auflösbarer Liealgebren, Lecture Notes in Math., vol. 357, Springer-Verlag, Berlin and New York, 1973.
  • [3] J. Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, fasc. 37, Gauthier-Villars, Paris, 1974. MR 0498737 (58:16803a)
  • [4] I. M. Gelfand and A. A. Kirillov, Sur les corps liés aux algèbres enveloppantes des algèbres de Lie, Inst. Hautes Etudes Sci. Publ. Math. No. 31 (1966), 5-19. MR 34 #7731. MR 0207918 (34:7731)
  • [5] N. Jacobson, Lie algebras, Interscience Tracts in Pure and Appl. Math., no. 10, Wiley, New York, 1962. MR 26 #1345. MR 0143793 (26:1345)
  • [6] -, Structure of rings, 2nd ed., Amer. Math. Soc. Colloq. Publ., vol. 37, Amer. Math. Soc., Providence, R. I., 1964. MR 36 #5158. MR 0222106 (36:5158)
  • [7] A. I. Ooms, On Lie algebras having a primitive universal enveloping algebra, J. Algebra 32 (1974), 488-500. MR 0387365 (52:8208)
  • [8] R. Rentschier and M. Vergne, Sur le semi-centre du corps enveloppant d'une algèbre de Lie, Ann. Sci. École Norm. Sup. (4) 6 (1973), 389-405. MR 50 # 13177. MR 0360730 (50:13177)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0430007-6
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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