Gel’fand, I. M.; Kirillov, A. A. The structure of the Lie field connected with a split semisimple Lie algebra. (English. Russian original) Zbl 0244.17007 Funct. Anal. Appl. 3, 6-21 (1969); translation from Funkts. Anal. Prilozh. 3, No. 1, 7-26 (1969). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 23 Documents MSC: 17B20 Simple, semisimple, reductive (super)algebras 17B35 Universal enveloping (super)algebras × Cite Format Result Cite Review PDF Full Text: DOI References: [1] I. M. Gel’fand and A. A. Kirillov, ”On fields connected with enveloping Lie algebras,” Dokl. Akad. Nauk SSSR,167, No. 3, 503-506 (1966). [2] I. M. Gel’fand and M. I. Graev, ”The Fourier transformation of rapidly decreasing functions on complex semisimple groups,” Dokl. Akad. Nauk SSSR,131, No. 3, 496-499 (1960). [3] B. Konstant, ”Lie group representations on polynomial rings,” Amer. J. Math.,85, No. 3, 327-404 (1963). · Zbl 0124.26802 · doi:10.2307/2373130 [4] I. M. Gel’fand and A. A. Kirillov, ”On the structure of the quotient field of the enveloping algebra of a semisimple Lie algebra,” Dokl. Akad. Nauk SSSR,180, No. 4, 775-777 (1961). [5] A. Borel and J. Tits, ”Groupes reductifs,” Publs. Math. Inst. des Hautes-Etudes Sci.,27, 55-151 (1965). · Zbl 0145.17402 · doi:10.1007/BF02684375 [6] J. Tits, ”Classification of algebraic semisimple groups,” Symposium,Boulder, Colorado (1965). · Zbl 0238.20052 [7] The Theory of Lie Algebras. The Topology of Lie Groups [Russian translation], IL, Moscow (1962). [8] A. Grothendieck, ”Eléments de géometrie algébrique. IV (Troisiéme partie),” Publs. Math. Inst. des Hautes-Etudes Sci.,28, 1-248 (1966). [9] N. Jacobson, Lie Algebras, Interscience, New York (1962). [10] Harish-Chandra, ”On some applications of the universal enveloping algebra of a semisimple Lie algebra,” Trans. Amer. Math. Soc.,70, 28-96 (1951). · Zbl 0042.12701 · doi:10.1090/S0002-9947-1951-0044515-0 [11] C. Chevalley, ”Invariants of finite groups generated by reflections,” Amer. J. Math.,77, No. 4, 778-782 (1955). · Zbl 0065.26103 · doi:10.2307/2372597 [12] I. M. Gel’fand and V. A. Ponomarev, ”The category of Harish-Chandra modules over the Lie algebra of the Lorentz group,” Dokl. Akad. Nauk SSSR,176, No. 2, 243-246 (1967). [For more detail see: Uspekhi Mat. Nauk,23, No. 2, 3-60 (1968)]. [13] I. M. Gel’fand and M. I. Graev, ”The geometry of homogeneous spaces, the representation of groups in homogeneous spaces, and related problems of integral geometry,” Trudy Mosk. Matem. Obshch.,8, 321-390 (1959). [14] I. M. Gel’fand, M. I. Graev, and I. I. Pyatetski-Shapiro, Generalized Functions. Vol. 6. The Theory of Representations and Automorphic Functions [in Russian], ”Nauka,” Moscow (1966). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.