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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

MSC:
17B35 Universal enveloping (super)algebras
17B20 Simple, semisimple, reductive (super)algebras
16W25 Derivations, actions of Lie algebras
16D25 Ideals in associative algebras
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[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
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