Diagrammes de Dynkin et algèbres enveloppantes d'algèbres de Lie semi-simples
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 31 (1998) no. 5, p. 631-657
@article{ASENS_1998_4_31_5_631_0,
     author = {Polo, Patrick},
     title = {Diagrammes de Dynkin et alg\`ebres enveloppantes d'alg\`ebres de Lie semi-simples},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {4e s{\'e}rie, 31},
     number = {5},
     year = {1998},
     pages = {631-657},
     doi = {10.1016/s0012-9593(98)80002-5},
     zbl = {0917.17006},
     mrnumber = {99h:17015},
     language = {fr},
     url = {http://www.numdam.org/item/ASENS_1998_4_31_5_631_0}
}
Polo, Patrick. Diagrammes de Dynkin et algèbres enveloppantes d'algèbres de Lie semi-simples. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 31 (1998) no. 5, pp. 631-657. doi : 10.1016/s0012-9593(98)80002-5. http://www.numdam.org/item/ASENS_1998_4_31_5_631_0/

[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). | MR 95m:16015 | Zbl 0823.17011

[2] H. Bass, Algebraic K-theory, Benjamin, London Amsterdam, 1968. | MR 40 #2736 | Zbl 0174.30302

[3] A. Beilinson et J. Bernstein, Localisation de g-modules, (C. R. Acad. Sc. Paris, t. 292, 1981, pp. 15-18). | MR 82k:14015 | Zbl 0476.14019

[4] W. Borho, Berechnung der Gelfand-Kirillov Dimension bei induzierte Darstellungen (Math. Annalen, Vol. 225, 1977, pp. 179-194). | MR 56 #12085 | Zbl 0346.17012

[5] W. Borho, On the Joseph-Small additivity principle for Goldie ranks (Compositio Math., Vol. 47, 1982, pp. 3-29). | Numdam | MR 84a:17007 | Zbl 0502.17007

[6] W. Borho et J. L. Brylinski, Differential Operators on Homogeneous Spaces. I (Invent. math., Vol. 69, 1982, pp. 437-476). | MR 84b:17007 | Zbl 0504.22015

[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). | MR 56 #12079 | Zbl 0327.17002

[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. | MR 82k:16020 | Zbl 0446.16001

[10] D.H. Collingwood et W. M. Mcgovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold, New York, 1993. | MR 94j:17001 | Zbl 0972.17008

[11] M. Demazure, Automorphismes et déformations des variétés de Borel (Inventiones math., Vol. 39, 1977, pp. 179-186). | MR 55 #8054 | Zbl 0406.14030

[12] J. Dixmier, Quotients simples de l'algèbre enveloppante de sl2 (J. Algebra, Vol. 24, 1973, pp. 551-564). | MR 46 #9134 | Zbl 0252.17004

[13] J. Dixmier, Algèbres Enveloppantes, Gauthier-Villars, Paris Bruxelles Montréal, 1974. | MR 58 #16803a | Zbl 0308.17007

[14] H. Hecht et D. Miličić, On the cohomological dimension of the localization functor (Proc. Amer. Math. Soc., Vol. 108, 1990, pp. 249-254). | MR 90d:17011 | Zbl 0714.22011

[15] H. Hiller, Geometry of Coxeter groups, Research Notes in Maths, Vol. 54, Pitman, Boston London Melbourne, 1982. | MR 83h:14045 | Zbl 0483.57002

[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). | MR 90b:17022 | Zbl 0672.17008

[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. | MR 94e:17007 | Zbl 0814.17008

[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). | MR 87g:17015 | Zbl 0588.17009

[19] J. C. Jantzen, Einhüllende Algebren halbeinfacher Lie Algebren, Springer-Verlag, Berlin Heidelberg New York, 1983. | Zbl 0541.17001

[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). | Numdam | MR 58 #809 | Zbl 0386.17004

[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). | MR 58 #22202 | Zbl 0401.17007

[22] A. Joseph, Kostant's Problem, Goldie Rank and the Gelfand-Kirillov Conjecture (Invent. Math., Vol. 56, 1980, pp. 191-213). | MR 82f:17008 | Zbl 0446.17006

[23] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra, I (J. Algebra, Vol. 65, 1980, pp. 284-306). | MR 82f:17009 | Zbl 0441.17004

[24] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra, III (J. Algebra, Vol. 73, 1981, pp. 295-326). | MR 83k:17010 | Zbl 0482.17002

[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. | MR 83m:17006 | Zbl 0468.17004

[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. | MR 88j:17008 | Zbl 0621.17006

[27] A. Joseph, A Sum Rule for Scale Factors in the Goldie Rank Polynomials (J. Algebra, Vol. 118, 1988, pp. 276-311). | MR 90a:17006 | Zbl 0699.17014

[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. | MR 98k:17011 | Zbl 0891.17007

[29] A. Joseph et L. W. Small, An additivity principle for Goldie rank (Israel J. Math., Vol. 31, 1978, pp. 105-114). | MR 80j:17005 | Zbl 0395.17010

[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). | MR 86a:17004 | Zbl 0543.17004

[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. | MR 86g:16001 | Zbl 0564.16001

[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). | MR 90i:17018 | Zbl 0691.16019

[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. | MR 92f:17010 | Zbl 0854.17011

[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. | MR 81j:16041 | Zbl 0449.16001

[35] S. Montgomery, Prime ideals in fixed rings (Comm. in Algebra, Vol. 9, 1981, pp. 423-449). | MR 82c:16034 | Zbl 0453.16019

[36] W. Soergel, The prime spectrum of the enveloping algebra of a reductive Lie algebra (Math. Z., Vol. 204, 1990, pp. 559-581). | MR 91d:17015 | Zbl 0685.17006

[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). | Numdam | MR 97e:17016 | Zbl 0871.17005

[38] A. Zahid, Les endomorphismes l-finis des modules de Whittaker (Bull. Soc. Math. France, t. 117, 1989, pp. 451-477). | Numdam | MR 91h:17010 | Zbl 0737.17005