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Minimal realizations and spectrum generating algebras. (English) Zbl 0285.17007

MSC:
17B35Universal enveloping Lie (super)algebras
17B10Representations of Lie algebras, algebraic theory
References:
[1]Ne’eman, Y.: Algebraic theory of particle physics, Chapter 10. New York: W. A. Benjamin 1967
[2]Barut, A. O.: Application of the dynamical group theory to the structure of the hadrons. Lectures in theoretical physics (Ed. Barut, A. O., Brittin, W. E.), Vol. 10B, pp. 377–426. New York: Gordon and Breach 1967
[3]Gelfand, I. M., Kirillov, A. A.: Inst. Hautes Etudes Sci. Publ. Math.31, 5 (1966) · Zbl 0144.02104 · doi:10.1007/BF02684800
[4]Jacobson, N.: Lie algebras. New York: Interscience 1962
[5]Joseph, A.: To appear
[6]Joseph, A.: Ann. Inst. H. Poincaré17, 325 (1972)
[7]Dixmier, J.: Algèbres enveloppantes, Chapter 3. Paris: Gauthier-Villars, in press
[8]Simoni, A., Zaccaria, F.: Nuovo Cimento59A, 280 (1969)
[9]Mukunda, N.: J. Math. Phys.8, 1069 (1967) · Zbl 0171.23801 · doi:10.1063/1.1705318
[10]Bourbaki, N.: Groupes et algèbres de Lie, Chapter 4–6. Paris: Hermann 1968
[11]Joseph, A.: A generalization of the Gelfand-Kirillov conjecture. Tel-Aviv University Preprint 385 (1973)
[12]Serre, J.-P.: Algèbres de Lie semi-simples complexes. Chapter VI, Theorem 4. New York: W. A. Benjamin 1966
[13]Conze, N.: Bull. Math. Soc. France, in press
[14]Coleman, S., Wess, J., Zumino, B.: Phys. Rev.177, 2239 (1969) · doi:10.1103/PhysRev.177.2239
[15]Joseph, A., Solomon, A. I.: J. Math. Phys.11, 748 (1970) · Zbl 0189.55201 · doi:10.1063/1.1665205
[16]Ndili, F. N.: Lett. Nuovo Cimento1, 13 (1971) · doi:10.1007/BF02785038
[17]Kleinert, H.: Group dynamics of the hydrogen atom. Lectures in theoretical physics (Ed. Barut, A. O., Brittin, W. E.), Vol. 10B, pp. 437–446. New York: Gordon and Breach 1967
[18]Joseph, A.: Proc. Camb. Phil. Soc., in press
[19]Goshen, S., Lipkin, H. J.: Ann. Phys.6, 301 (1959) · Zbl 0086.22301 · doi:10.1016/0003-4916(59)90066-1
[20]Lipkin, H. J.: Lie groups for pedestrians, p. 69. Amsterdam: North Holland Publ. Co. 1965
[21]Conze, N., Dixmier, J.: Bull. Sci. Math., 2 série96, 339 (1972)
[22]Helgason, N.: Differential geometry and symmetric spaces. Chapter III, Sections 4, 5. New York: Academic Press 1962
[23]Tits, J.: Inst. Hautes Etudes Sci. Publ. mathématiques31, 21 (1966) · Zbl 0145.25804 · doi:10.1007/BF02684801
[24]Bander, M., Itzykson, C.: Rev. Mod. Phys.38, 330 (1966) · doi:10.1103/RevModPhys.38.330
[25]Joseph, A.: J. Math. Phys.13, 351, Theorem 4.4 (1972) · Zbl 0238.17004 · doi:10.1063/1.1665983
[26]Dashen, R., Gell-Mann, M.: Phys. Letters17, 142 (1965) · doi:10.1016/0031-9163(65)90277-5