The minimal orbit in a simple Lie algebra and its associated maximal ideal
Joseph, A.
Annales scientifiques de l'École Normale Supérieure, Tome 9 (1976), p. 1-29 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1976_4_9_1_1_0,
     author = {Joseph, Anthony},
     title = {The minimal orbit in a simple Lie algebra and its associated maximal ideal},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {9},
     year = {1976},
     pages = {1-29},
     doi = {10.24033/asens.1302},
     mrnumber = {53 \#8168},
     zbl = {0346.17008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1976_4_9_1_1_0}
}

Joseph, A. The minimal orbit in a simple Lie algebra and its associated maximal ideal. Annales scientifiques de l'École Normale Supérieure, Tome 9 (1976) pp. 1-29. doi : 10.24033/asens.1302. http://gdmltest.u-ga.fr/item/ASENS_1976_4_9_1_1_0/

[1] L. Auslander and B. Kostant, Polarization and Unitary Representations of Solvable Lie Groups (Inv. Math., Vol. 14, 1971, pp.255-354). | MR 45 #2092 | Zbl 0233.22005

[2] P. Bernat, N. Conze et coll., Représentations des groupes de Lie résolubles, Monographies de la Société Mathématique de France, Dunod, Paris, 1972. | MR 56 #3183 | Zbl 0248.22012

[3] W. Borho (to appear).

[4] W. Borho und H. Kraft, Uber die Gelfand-Kirillov-Dimension Math. Annalen (to appear). | Zbl 0306.17005

[5] W. Borho, P. Gabriel und R. Rentschler, Primideale in Einhüllenden auflösbarer Lie-algebra (Lecture Notes in Math., Vol. 357, Springer Verlag, New York, 1973). | MR 51 #12965 | Zbl 0293.17005

[6] N. Bourbaki, Groupes et algèbres de Lie, Chap. IV-VI (Act. Sc. Ind., n° 1337, Hermann, Paris, 1968). | MR 39 #1590

[7] N. Conze, Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes (Bull. Soc. Math. France, Tome 102, 1974, pp. 379-415). | Numdam | MR 51 #10414 | Zbl 0298.17012

[8] N. Conze et J. Dixmier, Idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple (Bull. Sc. Math., Vol. 96, 1972, pp. 339-351). | MR 48 #356 | Zbl 0246.17009

[9] J. Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents IV (Canad. J. Math., Vol. 11, 1959, pp. 321-344). | MR 21 #5693 | Zbl 0125.06802

[10] J. Dixmier, Idéaux primitifs complètement premiers dans l'algèbre enveloppante de sl (3, C) In : Non-commutative Harmonic Analysis, Lecture Notes in Math., Vol. 466, Springer-Verlag, New York, 1975. | MR 52 #13962 | Zbl 0307.17005

[11] J. Dixmier, Algèbres enveloppantes (Cahiers scientifiques, Vol. 37, Gauthier-Villars, Paris, 1974). | MR 58 #16803a | Zbl 0308.17007

[12] E. B. Dynkin, Semisimple Subalgebras of Semisimple Lie Algebras [Mat. Sbornik N. S., Vol. 30 (72), 1952, pp. 349-463 (Eng. transl. Amer. Math. Soc. Transl., Vol. 6, 1957, p.p 111-244)]. | MR 13,904c | Zbl 0077.03404

[13] E. B. Dynkin, Maximal Subgroups of the Classical Groups [Trudy Moskov. Mat. Obšč, Vol. 1, 1952, pp. 39-166 (Eng. Transl. Amer. Math. Soc. Transl., Vol. 6, 1957, pp. 245-378). | Zbl 0077.03403

[14] A. G. Elashvili, Canonical Form and Stationary Subalgebras of Points of General Position for Simple Linear Lie Groups [Funkt. Analiz i Ego Prilozhen., Vol. 6, 1972, pp. 51-62 (Eng. Transl. Funct. Anal. appl., Vol. 6, 1972, pp. 44-53)]. | Zbl 0252.22015

[15] I. M. Gelfand et A. A. Kirillov, Sur les corps liés aux algèbres enveloppantes des algèbres de Lie (Inst. Hautes Études Scient., Publ. Math., n° 31, 1966, pp. 5-19). | Numdam | MR 34 #7731 | Zbl 0144.02104

[16 H. Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, n° 10, Interscience, New York, 1962. | Zbl 0121.27504

[17] A. Joseph, Derivations of Lie Brackets and Canonical Quantization (Commun. math. phys., Vol. 17. 1970, pp. 210-232). | MR 45 #3015 | Zbl 0194.58402

[18] A. Joseph, Gelfand-Kirillov Dimension for Algebras Associated with the Weyl Algebra (Ann. Inst, H. Poincaré, Vol. 17, 1972, p. 325). | Numdam | MR 49 #2868 | Zbl 0287.16011

[19] A. Joseph, A Generalization of the Gelfand-Kirillov Conjecture, Tel-Aviv Univ. Preprint 1973, TAUP-385-73.

[20] A. Joseph, Minimal Realizations and Spectrum Generating Algebras (Commun. math. phys., Vol. 36, 1974, pp. 325-338). | MR 49 #6795 | Zbl 0285.17007

[21] A. Joseph, Sur les algèbres de Weyl (Litheographed Lecture Notes, Inst. Hautes Études Scient., 1974).

[22] A. Joseph, The Gelfand-Kirillov Conjecture in Classical Mechanics and Quantization, Inst. Hautes Études Scient., preprint, 1974.

[23] V. G. Kac, Simple Irreducible Graded Lie Algebras of Finite Growth [Izv. Akad. Nauk S.S.S.R., Ser. Mat., Vol. 32, 1968, n° 6 (Eng. Transl. Math. U.S.S.R., Izvectija, Vol. 2, 1968, pp. 1271-1311)]. | MR 41 #4590 | Zbl 0222.17007

[24] F. I. Karpevelič, On Non-Semisimple Maximal Subalgebras of Semisimple Lie Algebras (Dokl. Akad. Nauk S.S.S.R. (N.S.), Vol. 76, 1951, pp. 775-778, Russian). | Zbl 0044.26303

[25] B. Kostant, The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group (Amer. J. Math., Vol. 81, 1959, pp. 973-1032). | MR 22 #5693 | Zbl 0099.25603

[26] B. Kostant, Lie Group Representations on Polynomial Rings (Amer. J. Math., Vol. 85, 1963, pp. 327-404). | MR 28 #1252 | Zbl 0124.26802

[27] B. Kostant, Quantization and Unitary Representations (Lecture Notes in Math., Vol. 170, Springer-Verlag, New York, 1970, pp. 87-208). | MR 45 #3638 | Zbl 0223.53028

[28] B. Kostant, Private communication.

[29] M. Lorente and B. Gruber, Classification of Semisimple Subalgebras of Simple Lie Algebras (J. Math. Phys., Vol. 13, 1972, pp. 1639-1663). | MR 46 #9241 | Zbl 0241.17006

[30] H. Ozeki and M. Wakimoto, On Polarizations of Certain Homogeneous Spaces (Hiroshima Math. J., Vol. 2, 1972, pp. 445-482). | MR 49 #5236a | Zbl 0267.22011

[31] W. Schmid, Die Randwerte Homomorpher Funktionen auf Hermitesch Symmetrischen Raumen (Inv. Math., Vol. 9, 1969/1970, pp. 61-80, footnote p. 79). | MR 41 #3806 | Zbl 0219.32013

[32] M. Vergne, La structure de Poisson sur l'algèbre symétrique d'une algèbre de Lie nilpotente (Bull. Soc. math. France, Tome 100, 1972, pp. 301-355). | Numdam | MR 52 #657 | Zbl 0256.17002

[33] J. Tits, Une remarque sur la structure des algèbres de Lie semi-simple complexes (Proc. Konninkl. Nederl. Akad. Wetenschappen, Series A, Vol. 63, 1960, pp. 48-53). | MR 22 #1633 | Zbl 0093.04001