Symplectic structure in the enveloping algebra of a Lie algebra
Bulletin de la Société Mathématique de France, Tome 102 (1974), pp. 75-83. 
@article{BSMF_1974__102__75_0,
     author = {Joseph, Anthony},
     title = {Symplectic structure in the enveloping algebra of a {Lie} algebra},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {75--83},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {102},
     year = {1974},
     doi = {10.24033/bsmf.1770},
     mrnumber = {50 #4678},
     zbl = {0291.17008},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.1770/}
}
TY  - JOUR
AU  - Joseph, Anthony
TI  - Symplectic structure in the enveloping algebra of a Lie algebra
JO  - Bulletin de la Société Mathématique de France
PY  - 1974
SP  - 75
EP  - 83
VL  - 102
PB  - Société mathématique de France
UR  - http://www.numdam.org/articles/10.24033/bsmf.1770/
DO  - 10.24033/bsmf.1770
LA  - en
ID  - BSMF_1974__102__75_0
ER  - 
%0 Journal Article
%A Joseph, Anthony
%T Symplectic structure in the enveloping algebra of a Lie algebra
%J Bulletin de la Société Mathématique de France
%D 1974
%P 75-83
%V 102
%I Société mathématique de France
%U http://www.numdam.org/articles/10.24033/bsmf.1770/
%R 10.24033/bsmf.1770
%G en
%F BSMF_1974__102__75_0
Joseph, Anthony. Symplectic structure in the enveloping algebra of a Lie algebra. Bulletin de la Société Mathématique de France, Tome 102 (1974), pp. 75-83. doi : 10.24033/bsmf.1770. http://www.numdam.org/articles/10.24033/bsmf.1770/

[1] Dixmier (J.). - Sur les représentations unitaires des groupes de Lie nilpotents, II., Bull. Soc. math. Fr., t. 85, 1957, p. 325-388. | EuDML | Numdam | MR | Zbl

[2] Gel'Fand (I. M.) and Kirillov (A. A.). - Fields associated with enveloping algebras of Lie algebras, Soviet Mathematics, t. 7, 1966, p. 407-409 [en russe] ; Doklady Akad. Nauk SSSR, t. 167, 1966, p. 503-505. | Zbl

[3] Gel'Fand (I. M.) and Kirillov (A. A.). - Sur les corps liés aux algèbres enveloppantes des algèbres de Lie. - Paris, Presses universitaires de France, 1966 (Institut des Hautes Études Scientifiques, Publications mathématiques, 31, p. 5-19). | EuDML | Numdam | MR | Zbl

[4] Gel'Fand (I. M.) and Kirillov (A. A.). - Structure of the Lie field connected with a split semisimple Lie algebra [en russe], Funkcional'nyj Analiz, t. 3, 1969, fasc. 1, p. 7-26. | MR | Zbl

[5] Helgason (S.). - Differential geometry and symmetric spaces. - New York, Academic Press, 1962 (Pure and applied Mathematics, Academic Press, 12). | MR | Zbl

[6] Jacobson (N.). - Lie algebras. - New York, Interscience Publishers, 1962 (Interscience Tracts in pure and applied Mathematics, 10). | Zbl

[7] Joseph (A.). - Commuting polynomials in quantum canonical operators and realizations of Lie algebras, J. of math. Phys., t. 13, 1972, p. 351-357. | MR | Zbl

[8] Joseph (A.). - Gel'fand-Kirillov dimension for algebras associated with the Weyl algebra, Ann. Inst. H. Poincaré, série A, t. 17, 1973, p. 325-336. | EuDML | Numdam | MR | Zbl

[9] Joseph (A.). - Proof of the Gel'fand-Kirillov conjecture for solvable Lie algebras, Proc. Amer. math. Soc. (à paraître). | Zbl

[10] Lang (S.). - Algebra. - New York, Addison-Wesley publishing Company, 1965 (Addison-Wesley Series in Mathematics). | MR | Zbl

[11] Nghiêm (X. H.). - Sur certains sous-corps commutatifs du corps enveloppant d'une algèbre de Lie résoluble, Bull. Sc. math., série 2, t. 96, 1972, p. 111-128. | Zbl

Cité par Sources :