On Lie algebras with primitive envelopes, supplements
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- by Alfons I. Ooms PDF
- Proc. Amer. Math. Soc. 58 (1976), 67-72 Request permission
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
- Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042 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.
- Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Fasc. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). MR 0498737
- I. M. Gelfand and A. A. Kirillov, Sur les corps liés aux algèbres enveloppantes des algèbres de Lie, Inst. Hautes Études Sci. Publ. Math. 31 (1966), 5–19 (French). MR 207918
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
- Alfons I. Ooms, On Lie algebras having a primitive universal enveloping algebra, J. Algebra 32 (1974), no. 3, 488–500. MR 387365, DOI 10.1016/0021-8693(74)90154-9
- Rudolf Rentschler and Michèle Vergne, Sur le semi-centre du corps enveloppant d’une algèbre de Lie, Ann. Sci. École Norm. Sup. (4) 6 (1973), 389–405 (French). MR 360730
Additional Information
- © Copyright 1976 American Mathematical Society
- 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