@article{ASENS_1976_4_9_1_1_0, author = {Joseph, A.}, title = {The minimal orbit in a simple {Lie} algebra and its associated maximal ideal}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {1--29}, publisher = {Elsevier}, volume = {Ser. 4, 9}, number = {1}, year = {1976}, doi = {10.24033/asens.1302}, mrnumber = {53 #8168}, zbl = {0346.17008}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.1302/} }
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 SP - 1 EP - 29 VL - 9 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.24033/asens.1302/ DO - 10.24033/asens.1302 LA - en ID - ASENS_1976_4_9_1_1_0 ER -
%0 Journal Article %A Joseph, A. %T The minimal orbit in a simple Lie algebra and its associated maximal ideal %J Annales scientifiques de l'École Normale Supérieure %D 1976 %P 1-29 %V 9 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.24033/asens.1302/ %R 10.24033/asens.1302 %G en %F 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, Série 4, Tome 9 (1976) no. 1, pp. 1-29. doi : 10.24033/asens.1302. http://archive.numdam.org/articles/10.24033/asens.1302/
[1] Polarization and Unitary Representations of Solvable Lie Groups (Inv. Math., Vol. 14, 1971, pp.255-354). | MR | Zbl
and ,[2] Représentations des groupes de Lie résolubles, Monographies de la Société Mathématique de France, Dunod, Paris, 1972. | MR | Zbl
, et coll.,[3]
(to appear).[4] Uber die Gelfand-Kirillov-Dimension Math. Annalen (to appear). | Zbl
und ,[5] Primideale in Einhüllenden auflösbarer Lie-algebra (Lecture Notes in Math., Vol. 357, Springer Verlag, New York, 1973). | MR | Zbl
, und ,[6] Groupes et algèbres de Lie, Chap. IV-VI (Act. Sc. Ind., n° 1337, Hermann, Paris, 1968). | MR
,[7] Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes (Bull. Soc. Math. France, Tome 102, 1974, pp. 379-415). | Numdam | MR | Zbl
,[8] Idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple (Bull. Sc. Math., Vol. 96, 1972, pp. 339-351). | MR | Zbl
et ,[9] Sur les représentations unitaires des groupes de Lie nilpotents IV (Canad. J. Math., Vol. 11, 1959, pp. 321-344). | MR | Zbl
,[10] 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 | Zbl
,[11] Algèbres enveloppantes (Cahiers scientifiques, Vol. 37, Gauthier-Villars, Paris, 1974). | MR | Zbl
,[12] 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 | Zbl
,[13] 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
,[14] 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
,[15] 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 | Zbl
et ,[16 Lie algebras, Interscience Tracts in Pure and Applied Mathematics, n° 10, Interscience, New York, 1962. | Zbl
,[17] Derivations of Lie Brackets and Canonical Quantization (Commun. math. phys., Vol. 17. 1970, pp. 210-232). | MR | Zbl
,[18] Gelfand-Kirillov Dimension for Algebras Associated with the Weyl Algebra (Ann. Inst, H. Poincaré, Vol. 17, 1972, p. 325). | Numdam | MR | Zbl
,[19] A Generalization of the Gelfand-Kirillov Conjecture, Tel-Aviv Univ. Preprint 1973, TAUP-385-73.
,[20] Minimal Realizations and Spectrum Generating Algebras (Commun. math. phys., Vol. 36, 1974, pp. 325-338). | MR | Zbl
,[21] Sur les algèbres de Weyl (Litheographed Lecture Notes, Inst. Hautes Études Scient., 1974).
,[22] The Gelfand-Kirillov Conjecture in Classical Mechanics and Quantization, Inst. Hautes Études Scient., preprint, 1974.
,[23] 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 | Zbl
,[24] 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
,[25] 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 | Zbl
,[26] Lie Group Representations on Polynomial Rings (Amer. J. Math., Vol. 85, 1963, pp. 327-404). | MR | Zbl
,[27] Quantization and Unitary Representations (Lecture Notes in Math., Vol. 170, Springer-Verlag, New York, 1970, pp. 87-208). | MR | Zbl
,[28]
, Private communication.[29] Classification of Semisimple Subalgebras of Simple Lie Algebras (J. Math. Phys., Vol. 13, 1972, pp. 1639-1663). | MR | Zbl
and ,[30] On Polarizations of Certain Homogeneous Spaces (Hiroshima Math. J., Vol. 2, 1972, pp. 445-482). | MR | Zbl
and ,[31] Die Randwerte Homomorpher Funktionen auf Hermitesch Symmetrischen Raumen (Inv. Math., Vol. 9, 1969/1970, pp. 61-80, footnote p. 79). | MR | Zbl
,[32] 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 | Zbl
,[33] 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 | Zbl
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