Hostname: page-component-76c49bb84f-t7r7g Total loading time: 0 Render date: 2025-07-12T16:05:33.430Z Has data issue: false hasContentIssue false
  • English
  • Français

Isomorphic exponential Weyl algebras

Published online by Cambridge University Press:  18 May 2009

P. L. Robinson
P. L. Robinson
Affiliation:
Department of Mathematics, University of Florida, Gainesville FL 32611, USA
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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].

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 7 - 10
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), 1669–1688.CrossRefGoogle Scholar
4.Manuceau, J., Sirugue, M., Testard, D., Verbeure, A., The smallest C*-algebra for canonical commutation relations, Comm. Math. Phys. 32 (1973), 231–243.CrossRefGoogle Scholar
5.McConnell, J. C. and Pettit, J. J., Crossed products and multiplicative analogues of Weyl algebras, J. London Math. Soc. 38 (1988), 47–55.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), 712–715.Google Scholar
7.Rieffel, M. A., C*-algebras associated with irrational rotations, Pacific J. Math. 93 (1981), 415–429.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), 351–354.Google Scholar