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A characterization theorem for realizations of sl(2)

Published online by Cambridge University Press:  24 October 2008

A. Joseph
A. Joseph
Affiliation:
Department of Physics and Astronomy, Tel-Aviv University, Ramat Aviv, Israel
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Abstract

Let A1 denote the algebra generated by one pair of canonical operators. It is shown that the realizations of sl(2) in A1 divide into two non-empty classes determined by the spectrum of the semisimple element of sl(2) in A1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 119 - 131
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Dixmier, J.Bull. Soc. Math. France, 96 (1968), 209.CrossRefGoogle Scholar
(2)Joseph, A.J. Math. and Phys. 13 (1970), 351.CrossRefGoogle Scholar
(3)Joseph, A.Amer. J. of Math. (in Press).Google Scholar
(4)Simoni, A. and Zaccaria, F.Nuovo Cimento 59A (1969), 280.CrossRefGoogle Scholar
(5)Jacobson, N.Lie Algebras (Intersoience; New York, 1966).Google Scholar
(6)Joseph, A.Ann. Inst. H. Poincaré 17A (1972), 325.Google Scholar
(7)Gelfand, I. M. and Kirillov, A. A.Institut des Hautes Etudes Scientifiques, Publication Mathelnatiques 31 (1966), 5.CrossRefGoogle Scholar
(8)Joseph, A.Comm. Math. Phys. 17 (1970), 210.CrossRefGoogle Scholar
(9)Dlxmier, J.Quotients simples de l'algèbre enveloppante de sl(2). J. of Algebra (in Press).Google Scholar