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On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra. (English. Russian original) Zbl 0283.17001

Funct. Anal. Appl. 6, 307-312 (1973); translation from Funkts. Anal. Prilozh. 6, No. 4, 65-70 (1972).

MSC:

17B35 Universal enveloping (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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References:

[1] I. N. Bernshtein, I. M. Gel’fand, and S. I. Gel’fand, ”The structure of representations generated by vectors of the highest weight,” Funktsional. Analiz i ego Prilozhen.,5, No. 1, 1-9 (1971). · Zbl 0246.17008
[2] I. M. Gel’fand and A. A. Kirillov, ”The structure of the Lie field connected with a semisimple decomposable Lie algebra,” Funktsional. Analiz i ego Prilozhen.,3, No. 1, 7-26 (1969).
[3] K. R. Parthasarathy, R. Ranga Rao, and V. S. Varadarajan, ”Representations of complex semisimple Lie groups and Lie algebras,” Ann. Math.,85, 383-429 (1967). · Zbl 0177.18004
[4] Theory of Lie Algebras. Topology of Lie Groups [in Russian], IL, Moscow (1962).
[5] N. Jacobson, Lie Algebras, Interscience, New York (1962).
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