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Isomorphic exponential Weyl algebras

Published online by Cambridge University Press:  18 May 2009

P. L. Robinson
Affiliation:
Department of Mathematics, University of Florida, Gainesville FL 32611, USA
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Canonically associated to a real symplectic vector space are several associative algebras. The Weyl algebra (generated by the Heisenberg commutation relations) has been the subject of much study; see [1] for example. The exponential Weyl algebra (generated by the canonical commutation relations in exponential form) has been less well studied; see [8].

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Dixmier, J., Enveloping algebras (North-Holland, 1977).Google Scholar
2.Emch, G. G., Algebraic methods in statistical mechanics and quantum field theory (Wiley Interscience, 1972).Google Scholar
3.Jategaonkar, V. A., A multiplicative analog of the Weyl algebra, Comm. Algebra 12 (1984), 16691688.CrossRefGoogle Scholar
4.Manuceau, J., Sirugue, M., Testard, D., Verbeure, A., The smallest C*-algebra for canonical commutation relations, Comm. Math. Phys. 32 (1973), 231243.CrossRefGoogle Scholar
5.McConnell, J. C. and Pettit, J. J., Crossed products and multiplicative analogues of Weyl algebras, J. London Math. Soc. 38 (1988), 4755.CrossRefGoogle Scholar
6.Rentschler, R. and Gabriel, P., Sur la dimension des anneaux et ensembles ordonnés, C. R. Acad Sci. Paris Sér I Math. 265 (1967), 712715.Google Scholar
7.Rieffel, M. A., C*-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), 415429.CrossRefGoogle Scholar
8.Robinson, P. L., The exponential Weyl algebra, preprint, 1988.Google Scholar
9.Roos, J. E., Propriétés homologiques des quotients primitifs des algèbres enveloppantes des algèbres de Lie semi-simples, C. R. Acad Sci. Paris Sér 1 Math. 276 (1973), 351354.Google Scholar