no. 5
Diagrammes de Dynkin et algèbres enveloppantes d'algèbres de Lie semi-simples
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 5, pp. 631-657 
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     title = {Diagrammes de {Dynkin} et alg\`ebres enveloppantes d'alg\`ebres de {Lie} semi-simples},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {631--657},
     year = {1998},
     publisher = {Elsevier},
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}
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Polo, Patrick. Diagrammes de Dynkin et algèbres enveloppantes d'algèbres de Lie semi-simples. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 5, pp. 631-657. doi: 10.1016/s0012-9593(98)80002-5

[1] J. Alev et P. Polo, A rigidity theorem for finite group actions on enveloping algebras of semisimple Lie algebras (Adv. in Math., Vol. 111, 1995, pp. 208-226). | Zbl | MR

[2] H. Bass, Algebraic K-theory, Benjamin, London Amsterdam, 1968. | Zbl | MR

[3] A. Beilinson et J. Bernstein, Localisation de g-modules, (C. R. Acad. Sc. Paris, t. 292, 1981, pp. 15-18). | Zbl | MR

[4] W. Borho, Berechnung der Gelfand-Kirillov Dimension bei induzierte Darstellungen (Math. Annalen, Vol. 225, 1977, pp. 179-194). | Zbl | MR

[5] W. Borho, On the Joseph-Small additivity principle for Goldie ranks (Compositio Math., Vol. 47, 1982, pp. 3-29). | Zbl | MR | Numdam

[6] W. Borho et J. L. Brylinski, Differential Operators on Homogeneous Spaces. I (Invent. math., Vol. 69, 1982, pp. 437-476). | Zbl | MR

[7] W. Borho et J. C. Jantzen, Über primitive Ideale in der Einhüllenden einer halbeinfacher Lie-Algebra (Invent. math., Vol. 39, 1977, pp. 1-53). | Zbl | MR

[8] N. Bourbaki, Groupes et algèbres de Lie, Chap. I, IV-VI, VII-VIII, Hermann, Paris, 1971, 1968, 1975.

[9] A. W. Chatters et C. R. Hajarnavis, Rings with chain conditions, Research Notes in Math., Vol. 44, Pitman, Boston London Melbourne, 1980. | Zbl | MR

[10] D.H. Collingwood et W. M. Mcgovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold, New York, 1993. | Zbl | MR

[11] M. Demazure, Automorphismes et déformations des variétés de Borel (Inventiones math., Vol. 39, 1977, pp. 179-186). | Zbl | MR

[12] J. Dixmier, Quotients simples de l'algèbre enveloppante de sl2 (J. Algebra, Vol. 24, 1973, pp. 551-564). | Zbl | MR

[13] J. Dixmier, Algèbres Enveloppantes, Gauthier-Villars, Paris Bruxelles Montréal, 1974. | Zbl | MR

[14] H. Hecht et D. Miličić, On the cohomological dimension of the localization functor (Proc. Amer. Math. Soc., Vol. 108, 1990, pp. 249-254). | Zbl | MR

[15] H. Hiller, Geometry of Coxeter groups, Research Notes in Maths, Vol. 54, Pitman, Boston London Melbourne, 1982. | Zbl | MR

[16] T. J. Hodges, K-Theory of D-modules and primitive factors of enveloping algebras of semisimple Lie algebras (Bull. Sc. math., T. 113, 1989, pp. 85-88). | Zbl | MR

[17] T. J. Hodges, Morita Equivalence of Primitive factors of U(sl(2)), pp. 175-179 in : Kazhdan-Lusztig theories and related topics (ed. V. Deodhar), Contemporary Maths, Vol. 139, 1992. | Zbl | MR

[18] T. J. Hodges et S. P. Smith, On the global dimension of certain primitive factors of the enveloping algebra of a semisimple Lie algebra (J. London Math. Soc., Vol. 32, 1985, pp. 411-418). | Zbl | MR

[19] J. C. Jantzen, Einhüllende Algebren halbeinfacher Lie Algebren, Springer-Verlag, Berlin Heidelberg New York, 1983. | Zbl

[20] A. Joseph, On the annihilators of the simple subquotients of the principal series (Ann. Scient. Éc. Norm. Sup., t. 10, 1977, pp. 419-440). | Zbl | MR | Numdam

[21] A. Joseph, Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules (J. London Math. Soc., Vol. 18, 1978, pp. 50-60). | Zbl | MR

[22] A. Joseph, Kostant's Problem, Goldie Rank and the Gelfand-Kirillov Conjecture (Invent. Math., Vol. 56, 1980, pp. 191-213). | Zbl | MR

[23] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra, I (J. Algebra, Vol. 65, 1980, pp. 284-306). | Zbl | MR

[24] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra, III (J. Algebra, Vol. 73, 1981, pp. 295-326). | Zbl | MR

[25] A. Joseph, Kostant's problem and Goldie rank, pp. 249-266 in : Non Commutative Harmonic Analysis and Lie Groups (éds. J. Carmona, M. Vergne), Lecture Notes in Math., Vol. 880, Springer-Verlag, Berlin Heidelberg New York, 1981. | Zbl | MR

[26] A. Joseph, On the Cyclicity of Vectors Associated with Duflo Involutions, pp. 144-188 in : Non Commutative Harmonic Analysis and Lie Groups (éds. J. Carmona, P. Delorme, M. Vergne), Lecture Notes in Math., Vol. 1243, Springer-Verlag, Berlin Heidelberg New York, 1987. | Zbl | MR

[27] A. Joseph, A Sum Rule for Scale Factors in the Goldie Rank Polynomials (J. Algebra, Vol. 118, 1988, pp. 276-311). | Zbl | MR

[28] A. Joseph, Coxeter structure and finite group action, pp. 185-219 in : Algèbre non commutative, groupes quantiques et invariants (éds. J. Alev, G. Cauchon), Soc. Math. France, 1997. | Zbl | MR

[29] A. Joseph et L. W. Small, An additivity principle for Goldie rank (Israel J. Math., Vol. 31, 1978, pp. 105-114). | Zbl | MR

[30] A. Joseph et J. T. Stafford, Modules of l-finite vectors over semisimple Lie algebras (Proc. London Math. Soc., Vol. 49, 1984, pp. 361-384). | Zbl | MR

[31] G. R. Krause et T. H. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Research Notes in Math., Vol. 116, Pitman, Boston London Melbourne, 1985. | Zbl | MR

[32] T. Levasseur et J. T. Stafford, Rings of differential operators on classical rings of invariants (Memoirs of the Amer. Math. Soc., Vol. 412, 1989). | Zbl | MR

[33] W. M. Mcgovern, Dixmier Algebras and the Orbit Method, pp. 397-416 in : Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (eds. A. Connes et al.), Progress in Math., Vol. 92, Birkhäuser, Boston Basel Berlin, 1990. | Zbl | MR

[34] S. Montgomery, Fixed Rings of Finite Automorphism Groups of Associative Rings, Lecture Notes in Math., Vol. 818, Springer-Verlag, Berlin Heidelberg New York, 1980. | Zbl | MR

[35] S. Montgomery, Prime ideals in fixed rings (Comm. in Algebra, Vol. 9, 1981, pp. 423-449). | Zbl | MR

[36] W. Soergel, The prime spectrum of the enveloping algebra of a reductive Lie algebra (Math. Z., Vol. 204, 1990, pp. 559-581). | Zbl | MR

[37] W. Soergel, Hochschild cohomology of regular maximal primitive quotients of enveloping algebras of semisimple Lie algebras (Ann. scient. Éc. Norm. Sup., t. 29, 1996, pp. 535-538). | Zbl | MR | Numdam

[38] A. Zahid, Les endomorphismes l-finis des modules de Whittaker (Bull. Soc. Math. France, t. 117, 1989, pp. 451-477). | Zbl | MR | Numdam

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