On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
Bulletin de la Société Mathématique de France (1979)
- Volume: 107, page 139-159
- ISSN: 0037-9484
Access Full Article
topHow to cite
topJoseph, Anthony. "On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case." Bulletin de la Société Mathématique de France 107 (1979): 139-159. <http://eudml.org/doc/87341>.
@article{Joseph1979,
author = {Joseph, Anthony},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Weyl Algebra; Primitive Ideals; Universal Enveloping Algebra; Ring Of Fractions; Gelfand-Kirillov Dimension; Complex Semisimple Lie Algebra},
language = {eng},
pages = {139-159},
publisher = {Société mathématique de France},
title = {On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case},
url = {http://eudml.org/doc/87341},
volume = {107},
year = {1979},
}
TY - JOUR
AU - Joseph, Anthony
TI - On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
JO - Bulletin de la Société Mathématique de France
PY - 1979
PB - Société mathématique de France
VL - 107
SP - 139
EP - 159
LA - eng
KW - Weyl Algebra; Primitive Ideals; Universal Enveloping Algebra; Ring Of Fractions; Gelfand-Kirillov Dimension; Complex Semisimple Lie Algebra
UR - http://eudml.org/doc/87341
ER -
References
top- [1] BORHO (W.). — Berechnung der Gel'fand-Kirillov-Dimension bei induzierten Darstellungen, Math. Annalen, t. 225, 1977, p. 177-194. Zbl0346.17012MR56 #12085
- [2] BORHO (W.). — Primitive vollprime Ideale in der Einhüllenden von so (5, C), J. of Algebra, t. 43, 1976, p. 619-654. Zbl0346.17013MR54 #10358
- [3] BORHO (W.), GABRIEL (P.) und RENTSCHLER (R.). — Primideale in Einhüllenden ausflösbarer Lie-algebren. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 357). Zbl0293.17005MR51 #12965
- [4] BORHO (W.) und JANTZEN (J. C.). — Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra, Invent. Math., Berlin, t. 39, 1977, p. 1-53. Zbl0327.17002MR56 #12079
- [5] BORHO (W.) und KRAFT (H.). — Über die Gel'fand-Kirillov-Dimension, Math. Annalen, t. 220, 1976, p. 1-24. Zbl0306.17005MR54 #367
- [6] CONZE (N.). — Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes, Bull. Soc. math. Fr., t. 102, 1974, p. 379-415. Zbl0298.17012MR51 #10414
- [7] CONZE-BERLINE (N.) et DUFLO (M.). — Sur les représentations induites des groupes semi-simples complexes, Compos. Math., Groningen, t. 34, 1977, p. 307-336. Zbl0389.22016MR55 #12872
- [8] DIXMIER (J.). — Algèbres enveloppantes, Paris, Gauthier-Villars, 1974 (Cahiers scientifiques, 37). Zbl0308.17007MR58 #16803a
- [9] DIXMIER (J.), DUFLO (M.) et VERGNE (M.). — Sur la représentation coadjointe d'une algèbre de Lie, Compos. Math., Groningen, t. 29, 1974, p. 309-323. Zbl0296.17009MR51 #630
- [10] DIXMIER (J.). — Polarisations dans les algèbres de Lie, II, Bull. Soc. math. France, t. 104, 1976, p. 145-164. Zbl0335.17002MR54 #12843
- [11] DUFLO (M.). — Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple, Annals of Math. Series 2, t. 105, 1977, p. 107-120. Zbl0346.17011MR55 #3013
- [12] GEL'FAND (I. M.) and KIRILLOV (A. A.). — On fields connected with the enveloping algebras of Lie algebras [in Russian], Dokl. Nauk S.S.S.R., t. 167, 1966, p. 503-505. Zbl0149.02903MR33 #4108
- [13] GEL'FAND (I. M.) and KIRILLOV (A. A.). — Sur les corps liés aux algèbres enveloppantes des algèbres de Lie. — Paris, Institut des hautes Études scientifiques, 1966 (Publications mathématiques, 31, p. 5-19). Zbl0144.02104MR34 #7731
- [14] GEL'FAND (I. M.) and KIRILLOV (A. A.). — The structure of the Lie field connected with a semisimple decomposable Lie algebra [in Russian], Funkcional Anal. i Prilozen., t. 3, 1969, p. 726. Zbl0244.17007MR39 #2827
- [15] JANTZEN (J. C.). — Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren, Math. Annalen, t. 226, 1977, p. 53-65. Zbl0372.17003MR55 #12783
- [16] JOSEPH (A.). — The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. scient. Ec. Norm. Sup., 4e serie, t. 9, 1976, p. 1-30. Zbl0346.17008MR53 #8168
- [17] JOSEPH (A.). — The algebraic method in representation theory (enveloping algebras), "Group theoretical methods in physics" [4, 1975, Nijmegen], p. 95-109. - Berlin, Springer-Verlag, 1976 (Lecture Notes in Physics, 50). Zbl0374.17003
- [18] JOSEPH (A.). A generalization of the Gel'fand-Kirillov conjecture, Amer. J. of Math., t. 99, 1977, p. 1151-1165. Zbl0378.17005MR57 #391
- [19] JOSEPH (A.). — Proof of the Gel'fand-Kirillov conjecture for solvable Lie algebras, Proc. Amer. math. Soc., t. 45, 1974, p. 1-10. Zbl0293.17006MR52 #522
- [20] JOSEPH (A.). — A preparation theorem for the prime spectrum of a semisimple Lie algebra, J. of Algebra, t. 48, 1977, p. 241-289. Zbl0405.17007MR56 #12082
- [21] JOSEPH (A.). — Primitive ideals in the enveloping algebras of sl (3) and sp (4), 1976 (unpublished).
- [22] JOSEPH (A.). — Sur les algèbres de Weyl, Lecture notes, 1974, (unpublished).
- [23] JOSEPH (A.). — Towards the Jantzen conjecture, Compos. Math., Groningen (in the press). Zbl0424.17004
- [24] JOSEPH (A.). — Gel'fand-Kirillov dimension for the annihilators of simple quotients of Verma modules. J. London math. Soc., t. 18, 1978, p. 50-60. Zbl0401.17007MR58 #22202
- [25] MCCONNELL (J. C.). — Representations of solvable Lie algebras and the Gel'fand-Kirillov conjecture, Proc. London math. Soc., Series 3, t. 29, 1974, p. 453-484. Zbl0323.17005MR50 #9997
- [26] NGHIÊM (X. H.). — Sur certains sous-corps commutatifs du corps enveloppant d'une algèbre de Lie résoluble, Bull. Sc. math., 2e série, t. 96, 1972, p. 111-128. Zbl0239.17007
- [27] NGHIÊM (X. H.). — Sur certaines représentations d'une algèbre de Lie résoluble complexe, Bull. Sc. math., 2e série, t. 97, 1973, p. 105-128. Zbl0275.17003
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.