Symplectic structure in the enveloping algebra of a Lie algebra

Anthony Joseph

Bulletin de la Société Mathématique de France (1974)

  • Volume: 102, page 75-83
  • ISSN: 0037-9484

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Joseph, Anthony. "Symplectic structure in the enveloping algebra of a Lie algebra." Bulletin de la Société Mathématique de France 102 (1974): 75-83. <http://eudml.org/doc/87240>.

@article{Joseph1974,
author = {Joseph, Anthony},
journal = {Bulletin de la Société Mathématique de France},
language = {eng},
pages = {75-83},
publisher = {Société mathématique de France},
title = {Symplectic structure in the enveloping algebra of a Lie algebra},
url = {http://eudml.org/doc/87240},
volume = {102},
year = {1974},
}

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
PB - Société mathématique de France
VL - 102
SP - 75
EP - 83
LA - eng
UR - http://eudml.org/doc/87240
ER -

References

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  1. [1] DIXMIER (J.). — Sur les représentations unitaires des groupes de Lie nilpotents, II., Bull. Soc. math. Fr., t. 85, 1957, p. 325-388. Zbl0085.10303MR20 #1928
  2. [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. Zbl0149.02903
  3. [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). Zbl0144.02104MR34 #7731
  4. [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. Zbl0244.17007MR39 #2827
  5. [5] HELGASON (S.). — Differential geometry and symmetric spaces. — New York, Academic Press, 1962 (Pure and applied Mathematics, Academic Press, 12). Zbl0111.18101MR26 #2986
  6. [6] JACOBSON (N.). — Lie algebras. — New York, Interscience Publishers, 1962 (Interscience Tracts in pure and applied Mathematics, 10). Zbl0121.27504
  7. [7] JOSEPH (A.). — Commuting polynomials in quantum canonical operators and realizations of Lie algebras, J. of math. Phys., t. 13, 1972, p. 351-357. Zbl0238.17004MR45 #6292
  8. [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. Zbl0287.16011MR49 #2868
  9. [9] JOSEPH (A.). — Proof of the Gel'fand-Kirillov conjecture for solvable Lie algebras, Proc. Amer. math. Soc. (à paraître). Zbl0293.17006
  10. [10] LANG (S.). — Algebra. — New York, Addison-Wesley publishing Company, 1965 (Addison-Wesley Series in Mathematics). Zbl0193.34701MR33 #5416
  11. [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. Zbl0239.17007

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