zbMATH — the first resource for mathematics

The prime spectrum of the enveloping algebra of a reductive Lie algebra. (English) Zbl 0685.17006
We describe the prime spectrum of the enveloping algebra of a reductive Lie algebra as a set and obtain a partial description of the Jacobson topology. Sheaves of differential operators play a key role and are also investigated in their own right.
Reviewer: W.Soergel

17B35 Universal enveloping (super)algebras
17B20 Simple, semisimple, reductive (super)algebras
16W25 Derivations, actions of Lie algebras
16D25 Ideals in associative algebras
Full Text: DOI EuDML
[1] [BB1] Borho, W., Brylinski, J.-L.: Differential operators on homogeneous spaces I. Invent. Math.69, 437–476 (1982) · Zbl 0504.22015 · doi:10.1007/BF01389364
[2] [BB2] Borho, W., Brylinski, J.-L.: Differential operators on homogeneous spaces II. Relative enveloping algebras. Bull. Soc. Math. Fr.117, 167–210 (1989) · Zbl 0702.22019
[3] [BJ] Borho, W., Jantzen, J.C.: Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra. Invent. Math.39, 1–53 (1977) · Zbl 0339.17006 · doi:10.1007/BF01695950
[4] [Bo] Borho, W.: Recent advances in enveloping algebras of semisimple Lie algebras. In: Séminaire Bourbaki 489. (Lect. Notes Math., vol. 677) Berlin Heidelberg New York: Springer 1978 · Zbl 0394.17005
[5] [Bou] Bourbaki, N.: Groupes et algèbres de Lie 4–6. Paris: Hermann 1968
[6] [CH] Chatters, A.W., Hajarnavis, C.R.: Rings with chain conditions. Boston London Melbourne: Pitman 1980 · Zbl 0446.16001
[7] [Dix] Dixmier, J.: Algèbres envelopantes. Paris Bruxelles Montréal: Gauthier-Villars 1974
[8] [Ha] Harthshorne, R.: Algebraic geometry. New York Heidelberg Berlin: Springer 1977
[9] [Ja1] Jantzen, J.C.: Moduln mit einem höchsten Gewicht. (Lect. Notes Math., vol. 750) Berlin Heidelberg New York: Springer 1979) · Zbl 0426.17001
[10] [Ja2] Jantzen, J.C.: Einhüllende Algebren halbeinfacher Lie-Algebren. Berlin Heidelberg New York: Springer 1983 · Zbl 0541.17001
[11] [Mo] Montgomery, S.: Prime ideals in fixed rings. Commun. Algebra9, 423–449 (1981) · Zbl 0453.16019 · doi:10.1080/00927878108822591
[12] [So] Soergel, W.: Universelle versus relative Einhüllende: Eine geometrische Untersuchung von Quotienten von universellen Einhüllenden halbeinfacher Lie-Algebren. Math. Ann.284, 177–198 (1989) · Zbl 0649.17012 · doi:10.1007/BF01442871
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.