Joseph, A. A preparation theorem for the prime spectrum of a semisimple Lie algebra. (English) Zbl 0405.17007 J. Algebra 48, 241-289 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 63 Documents MSC: 17B35 Universal enveloping (super)algebras 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras 16Kxx Division rings and semisimple Artin rings 16P60 Chain conditions on annihilators and summands: Goldie-type conditions Keywords:Preparation Theorem; Prime Spectrum; Semisimple Lie Algebra; Enveloping Algebra; Gelfand-Kirillov Conjecture × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Borho, W., Berechnung der Gelfand-Kirillov-Dimension bei induzierten Darstel-lungen, Math. Ann., 225, 177-194 (1977) · Zbl 0346.17012 [2] Borho, W.; Kraft, H., Über die Gelfand-Kirillov-Dimension, Math. Ann., 220, 1-24 (1976) · Zbl 0306.17005 [3] Borho, W., Primitive vollprime Ideale in der Einhüllenden von so \((5, C)\), J. Algebra, 43, 619-654 (1976) · Zbl 0346.17013 [4] Borho, W.; Gabriel, P.; Rentschler, R., Primideale in Einhüllenden ausflösbarer Lie-Algebren, (Lecture Notes in Mathematics, No. 357 (1973), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0293.17005 [5] Borho, W.; Rentschler, R., Oresche Teilmengen in Einhüllenden Algebren, Math. Ann., 217, 201-210 (1975) · Zbl 0297.17004 [6] Bourbaki, N., Groupes et algèbres de Lie, (Act. Sci. Ind., No. 1337 (1968), Hermann: Hermann Paris), Chaps. IV-VI · Zbl 0483.22001 [7] Conze, N., Algèbres d’opérateurs différentiels et quotients des algèbres enveloppantes, Bull. Soc. Math. France, 102, 379-415 (1974) · Zbl 0298.17012 [8] Dixmier, J., Sur les représentations unitaires des groupes de Lie nilpotents II, Bull. Soc. Math. France, 85, 325-388 (1957) · Zbl 0085.10303 [9] Dixmier, J., Sur les représentations unitaires des groupes de Lie nilpotents IV, Can. J. Math., 11, 321-344 (1959) · Zbl 0125.06802 [10] Dixmier, J., Algèbres enveloppantes, (cahiers scientifiques, No. 37 (1974), Gauthier-Villars: Gauthier-Villars Paris) · Zbl 0422.17003 [11] Dixmier, J., Idéaux primitifs complètement premiers dans l’algèbre enveloppante de sl \((3,C)\), (Non-Commutative Harmonic Analysis. Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics, No. 466 (1976), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New-York), 38-55 [12] Hadziev, Dz., Math. USSR Sb., 1, 383-396 (1967), Eng. Translation: · Zbl 0335.06014 [13] Jacobson, N., Lie algebras, (Interscience Tracts in Pure and Applied Mathematics, No. 10 (1962), Interscience: Interscience New York) · JFM 61.1044.02 [14] Joseph, A., Proof of the Gelfand-Kirillov conjecture for solvable Lie algebras, (Proc. Amer. Math. Soc., 45 (1974)), 1-10 · Zbl 0293.17006 [15] Joseph, A., The Gelfand-Kirillov Conjecture in Classical Mechanics and Quantization (1974), IHES, preprint [16] A. JosephAmer. J. Math.; A. JosephAmer. J. Math. · Zbl 0378.17005 [17] Joseph, A., The Minimal Orbit in a Simple Lie Algebra and its Associated Maximal Ideal, Ann. Scient. École Norm. Sup. Sér. \(4^e, 9, 1-30 (1976)\) · Zbl 0346.17008 [18] A. JosephAmer. J. Math.; A. JosephAmer. J. Math. · Zbl 0378.17006 [19] Joseph, A., The algebraic method in representation theory (enveloping algebras), (Janner, A., Proceedings of the Fourth International Colloquium on Group Theoretical Methods in Physics. Proceedings of the Fourth International Colloquium on Group Theoretical Methods in Physics, Nijmegen (1975)) · Zbl 0374.17003 [20] Joseph, A., Gelfand-Kirillov dimension for algebras associated with the Weyl algebra, Ann. Inst. H. Poincaré sect. A, 17, 325-336 (1972) · Zbl 0287.16011 [21] Kostant, B., Lie group representations on polynomial rings, Amer. J. Math., 85, 327-404 (1963) · Zbl 0124.26802 [22] McConnell, J. C., Representations of solvable Lie groups and the Gelfand-Kirillov conjecture, (Proc. London Math. Soc., 29 (1974)), 153-484 · Zbl 0323.17005 [23] Ozeki, H.; Wakimoto, M., On polarizations of certain homogeneous spaces, Hiroshima Math. J., 2, 445-482 (1972) · Zbl 0267.22011 [24] Rentschler, R.; Vergne, M., Sur le semi-centre du corps enveloppante d’une algèbre de Lie, Ann. Scient. École Norm. Sup. Sér. \(4^e, 6, 389-405 (1973)\) · Zbl 0293.17007 [25] Schmidt, W., Die Randwerte homomorpher Funktionen auf Hermitesch symmetrischen Raumen, Invent. Math., 9, 61-80 (1969/1970), (footnote p. 79) · Zbl 0219.32013 [26] Vergne, M., La structure de Poisson sur l’algèbre symétrique d’une algèbre de Lie nilpotente, Bull. Soc. Math. France, 100, 301-335 (1972) · Zbl 0256.17002 [27] N. Conze-Berline and M. DufloCompos. Math.; N. Conze-Berline and M. DufloCompos. Math. · Zbl 0389.22016 [28] Joseph, A., Sur les vecteurs de plus haut poids dans l’algèbre enveloppante d’une algèbre de Lie semi-simple complexe, C. R. Acad. Sci. Paris Ser. A, 281, 835-837 (1975) · Zbl 0321.17004 [29] Joseph, A., Primitive Ideals in the Enveloping Algebras of sl \((3,C)\) and sp \((4,C) (1976)\), preprint, Orsay [30] Joseph, A., On the Gelfand-Kirillov Conjecture for Induced Ideals in the Semisimple Case (1976), preprint, Orsay [31] Samuel, P., Anneaux factoriels (1963), Publications of the Mathematical Society of Sao Paulo: Publications of the Mathematical Society of Sao Paulo A. Oshira, Brazil · Zbl 0145.27404 [32] Dixmier, J., Idéaux primitifs dans les algèbres enveloppantes (1976), preprint, Paris · Zbl 0366.17007 [33] Duflo, M., Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple, Ann. Math., 105, 107-120 (1977) · Zbl 0346.17011 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.