The minimal orbit in a simple Lie algebra and its associated maximal ideal
Annales scientifiques de l'École Normale Supérieure (1976)
- Volume: 9, Issue: 1, page 1-29
- ISSN: 0012-9593
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topJoseph, A.. "The minimal orbit in a simple Lie algebra and its associated maximal ideal." Annales scientifiques de l'École Normale Supérieure 9.1 (1976): 1-29. <http://eudml.org/doc/81975>.
@article{Joseph1976,
author = {Joseph, A.},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {1},
pages = {1-29},
publisher = {Elsevier},
title = {The minimal orbit in a simple Lie algebra and its associated maximal ideal},
url = {http://eudml.org/doc/81975},
volume = {9},
year = {1976},
}
TY - JOUR
AU - Joseph, A.
TI - The minimal orbit in a simple Lie algebra and its associated maximal ideal
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1976
PB - Elsevier
VL - 9
IS - 1
SP - 1
EP - 29
LA - eng
UR - http://eudml.org/doc/81975
ER -
References
top- [1] L. AUSLANDER and B. KOSTANT, Polarization and Unitary Representations of Solvable Lie Groups (Inv. Math., Vol. 14, 1971, pp.255-354). Zbl0233.22005MR45 #2092
- [2] P. BERNAT, N. CONZE et coll., Représentations des groupes de Lie résolubles, Monographies de la Société Mathématique de France, Dunod, Paris, 1972. Zbl0248.22012MR56 #3183
- [3] W. BORHO (to appear).
- [4] W. BORHO und H. KRAFT, Uber die Gelfand-Kirillov-Dimension Math. Annalen (to appear). Zbl0306.17005
- [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). Zbl0293.17005MR51 #12965
- [6] N. BOURBAKI, Groupes et algèbres de Lie, Chap. IV-VI (Act. Sc. Ind., n° 1337, Hermann, Paris, 1968). MR39 #1590
- [7] N. CONZE, Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes (Bull. Soc. Math. France, Tome 102, 1974, pp. 379-415). Zbl0298.17012MR51 #10414
- [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). Zbl0246.17009MR48 #356
- [9] J. DIXMIER, Sur les représentations unitaires des groupes de Lie nilpotents IV (Canad. J. Math., Vol. 11, 1959, pp. 321-344). Zbl0125.06802MR21 #5693
- [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. Zbl0307.17005MR52 #13962
- [11] J. DIXMIER, Algèbres enveloppantes (Cahiers scientifiques, Vol. 37, Gauthier-Villars, Paris, 1974). Zbl0308.17007MR58 #16803a
- [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)]. Zbl0077.03404MR13,904c
- [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). Zbl0077.03403
- [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)]. Zbl0252.22015
- [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). Zbl0144.02104MR34 #7731
- [16 H. JACOBSON, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, n° 10, Interscience, New York, 1962. Zbl0121.27504
- [17] A. JOSEPH, Derivations of Lie Brackets and Canonical Quantization (Commun. math. phys., Vol. 17. 1970, pp. 210-232). Zbl0194.58402MR45 #3015
- [18] A. JOSEPH, Gelfand-Kirillov Dimension for Algebras Associated with the Weyl Algebra (Ann. Inst, H. Poincaré, Vol. 17, 1972, p. 325). Zbl0287.16011MR49 #2868
- [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). Zbl0285.17007MR49 #6795
- [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)]. Zbl0222.17007MR41 #4590
- [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). Zbl0044.26303
- [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). Zbl0099.25603MR22 #5693
- [26] B. KOSTANT, Lie Group Representations on Polynomial Rings (Amer. J. Math., Vol. 85, 1963, pp. 327-404). Zbl0124.26802MR28 #1252
- [27] B. KOSTANT, Quantization and Unitary Representations (Lecture Notes in Math., Vol. 170, Springer-Verlag, New York, 1970, pp. 87-208). Zbl0223.53028MR45 #3638
- [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). Zbl0241.17006MR46 #9241
- [30] H. OZEKI and M. WAKIMOTO, On Polarizations of Certain Homogeneous Spaces (Hiroshima Math. J., Vol. 2, 1972, pp. 445-482). Zbl0267.22011MR49 #5236a
- [31] W. SCHMID, Die Randwerte Homomorpher Funktionen auf Hermitesch Symmetrischen Raumen (Inv. Math., Vol. 9, 1969/1970, pp. 61-80, footnote p. 79). Zbl0219.32013MR41 #3806
- [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). Zbl0256.17002MR52 #657
- [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). Zbl0093.04001MR22 #1633
Citations in EuDML Documents
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- Didier Arnal, Hádi Benamor, Benjamin Cahen, Minimal realizations of classical simple Lie algebras through deformations
- Nicole Conze-Berline, Michel Duflo, Sur les représentations induites des groupes semi-simples complexes
- R. El Assoudi, J. Gauthier, I. Kupka, Controllability of right invariant systems on semi-simple Lie groups
- R. El Assoudi, J. P. Gauthier, I. A. K. Kupka, On subsemigroups of semisimple Lie groups
- Jean-Philippe Michel, Higher symmetries of the Laplacian via quantization
- Aboubeker Zahid, Les endomorphismes -finis des modules de Whittaker
- Walter Borho, Recent advances in enveloping algebras of semi-simple Lie-algebras
- Anthony Joseph, On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
- Anthony Joseph, Orbital varietes of the minimal orbit
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