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Some remarks about the associated envelope of a Lie algebra. (English. Russian original) Zbl 0227.22020

Funct. Anal. Appl. 1, 91-102 (1967); translation from Funkts. Anal. Prilozh. 1, No. 2, 1-14 (1967).

MSC:

22E60 Lie algebras of Lie groups
17B35 Universal enveloping (super)algebras
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References:

[1] I. M. Gel’fand and G. E. Shilov, Theory of Generalized Functions [in Russian], Moscow, Fizmatgiz, No. 1 (1958). · Zbl 0091.11103
[2] F. A. Berezin, On one representation of operators with the aid of functionals, Trudy Mosk. Matem. O-va, 17, 118-184 (1967).
[3] I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Derivatives [in Russian], Moscow, Fizmatgiz (1963). · Zbl 0102.24703
[4] I. M. Gel’fand, Center of an infinitesimal group ring, Matem. sb.,16, No. 1 (1950).
[5] F. A. Berezin, Laplace operators on semisimple Lie groups and certain symmetric spaces, UMN, 12, No. 1, 152-156 (1957).
[6] F. A. Berezin and I. M. Gel’fand, Certain remarks on the theory of spherical functions on symmetric Riemann manifolds, Trudy Mosk. Matem. O-va,5, 311-351 (1956).
[7] F. A. Berezin, Laplace operators on semisimple Lie groups, Trudy Mosk. Matem. O-va,6, 371-463 (1957). · Zbl 0091.28201
[8] Harish-Chandra, The characters of semisimple Lie groups, Trans. Amer. Math. Soc.,83, 98-163 (1956). · Zbl 0072.01801
[9] Harish-Chandra, Spherical functions on a semisimple Lie group I, Amer. J. Math,80 (1958). · Zbl 0093.12801
[10] Harish-Chandra, On some applications of the universal enveloping algebra of a semisimple Lie group algebra, Trans. Amer. Math. Soc.,70, 28-96 (1951). · Zbl 0042.12701
[11] A. M. Perelomov and V. S. Popov, Casimir operators for the groups U(n) and SU (n), Yadernaya Fizika,3, No. 5, 924-931
[12] A. M. Perelomov and V. S. Popov, Casimir operators for orthogonal groups, Yadernaya Fizika,3, No. 6, 1127-1134.
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