## On some applications of the universal envelopping algebra of a semisimple Lie algebra.(English)Zbl 0042.12701

### Keywords:

functional analysis
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### References:

 [1] Garrett Birkhoff, Representability of Lie algebras and Lie groups by matrices, Ann. of Math. (2) 38 (1937), no. 2, 526 – 532. · JFM 63.0090.01 [2] E. Cartan, Les groupes projectifs qui ne laissent invariante aucune multiplicité plane, Bull. Soc. Math. France 41 (1913), 53 – 96 (French). · JFM 44.0170.02 [3] Claude Chevalley, Sur la classification des algèbres de Lie simples et de leurs représentations, C. R. Acad. Sci. Paris 227 (1948), 1136 – 1138 (French). · Zbl 0034.17001 [4] Claude Chevalley, An algebraic proof of a property of Lie groups, Amer. J. Math. 63 (1941), 785 – 793. · Zbl 0026.06001 [5] Claude Chevalley, Algebraic Lie algebras, Ann. of Math. (2) 48 (1947), 91 – 100. · Zbl 0032.25202 [6] -, Theory of Lie groups, Princeton University Press, 1946. [7] I. M. Gel$$^{\prime}$$fand and M. A. Naĭmark, On the connection between the representations of a complex semi-simple Lie group and those of its maximal compact subgroups, Doklady Akad. Nauk SSSR (N.S.) 63 (1948), 225 – 228 (Russian). [8] Lars Gårding, Note on continuous representations of Lie groups, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 331 – 332. · Zbl 0031.05703 [9] Harish-Chandra, On representations of Lie algebras, Ann. of Math. (2) 50 (1949), 900 – 915. · Zbl 0035.01901 [10] Kenkichi Iwasawa, On some types of topological groups, Ann. of Math. (2) 50 (1949), 507 – 558. · Zbl 0034.01803 [11] F. I. Mautner, Ann. of Math. vol. 52 (1951) pp. 528-556. · Zbl 0039.02201 [12] H. Weyl, Math. Zeit. vol. 24 (1925) pp. 328-395. [13] -, The classical groups, Princeton University Press, 1939. [14] E. Witt, J. Reine Angew. Math. vol. 177 (1937) pp. 152-160.
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