A class of Lie and Jordan algebras realized by means of the canonical commutation relations
Annales de l'I.H.P. Physique théorique, Volume 14 (1971) no. 2, p. 179-188
@article{AIHPA_1971__14_2_179_0,
     author = {Tilgner, Hans},
     title = {A class of Lie and Jordan algebras realized by means of the canonical commutation relations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {2},
     year = {1971},
     pages = {179-188},
     zbl = {0211.35604},
     mrnumber = {289594},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1971__14_2_179_0}
}
Tilgner, Hans. A class of Lie and Jordan algebras realized by means of the canonical commutation relations. Annales de l'I.H.P. Physique théorique, Volume 14 (1971) no. 2, pp. 179-188. http://www.numdam.org/item/AIHPA_1971__14_2_179_0/

[1] H. Tilgner, A class of solvable Lie groups and their relation to the canonical formalism. Ann. Inst. H. Poincaré, Section A : Physique théorique, t. 13, n° 2, 1970. | Numdam | MR 277192

[2] H. Tilgner, A spectrum generating nilpotent group for the relativistic free particle. Ann. Inst. H. Poincaré, Section A : Physique théorique, t. 13, n° 2, 1970. | Numdam | MR 286389

[3] I. Segal, Quantized differential forms. Topology, t. 7, 1968, p. 147-172. | MR 232790 | Zbl 0162.40602

[4] J. Williamson, The exponential representation of canonical matrices. Am. J. Math., t. 61, 1939, p. 897-911. | MR 220 | Zbl 0022.10007

[5] M. Koecher, Jordan algebras and their applications. University of Minnesota notes, Minneapolis, 1962. | Zbl 0128.03101

[6] M. Koecher, Gruppen und Lie-Algebren von rationalen Funktionen. Math. Z., t. 109, 1969, p. 349-392. | MR 251092 | Zbl 0181.04503

[7] M. Koecher, An elementary approach to bounded symmetric domains. Rice University, Houston, Texas, 1969. | MR 261032 | Zbl 0217.10901

[8] J. Schwinger, On angular momentum, In Quantum theory of angular momentum. Edited by L. C. Biedenharn, H. van Dam, Academic Press, New York, 1965. | MR 198829

[9] C.P. Enz, Representation of group generators by boson or fermion operators. Application to spin perturbation. Helv. Phys. Acta, t. 39, 1966, p. 463-465.

[10] H.D. Döbner and T. Palev, Realizations of Lie algebras by rational functions of canonical variables. In « Proceedings of the IX. Internationale Universitätswochen für Kernphysik, 1970 in Schladming, Austria ». Springer Wien, to appear, 1970. | Zbl 0215.38504

[11] O. Loos, Symmetric spaces, I : General theory. Benjamin New York, 1969. | MR 239005 | Zbl 0175.48601

[12] O. Loos, Symmetric spaces, II : Compact spaces and classification. Benjamin, New York, 1969. | MR 239006 | Zbl 0175.48601

[13] S. Lang, Algebra. Addison-Wesley, Reading Mass, 1965. | MR 197234 | Zbl 0193.34701

[14] C. Chevalley, The construction and study of certain important algebras. The International Society of Japan, Tokio, 1955. | MR 72867 | Zbl 0065.01901