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The structure of exponential Weyl algebras

Part of: Rings and algebras arising under various constructions Modules, bimodules and ideals Conditions on elements

Published online by Cambridge University Press:  09 April 2009

P. L. Robinson
P. L. Robinson
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
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Abstract

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We present structural properties of the complex associative algebra generated by the canonical commutation relations in exponential form. In particular, we show it to be a central simple algebra that lacks zero divisors and is not Noetherian on either side; in addition, we determine explicitly its units and its automorphisms.

MSC classification

Secondary: 16D30: Infinite-dimensional simple rings (except as in ) 16S35: Twisted and skew group rings, crossed products 16U60: Units, groups of units
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 3 , December 1993 , pp. 302 - 310
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Dixmier, J., Enveloping algebras (North-Holland, Amsterdam, 1977).Google Scholar
[2]Jategaonkar, V. A., ‘A multiplicative analog of the Weyl algebra’, Comm. Algebra 12 (1984), 1669–1688.CrossRefGoogle Scholar
[3]Manuceau, J., C*-algèbre des relations de commutation’, Ann. Inst. H. Poincaré (A) 8 (1968), 139–161.Google Scholar
[4]Manuceau, J., Sirugue, M., Testard, D. and Verbeure, A., ‘The smallest C*-algebra for canonical commutation relations’, Comm. Math. Phys. 32 (1973), 231–243.Google 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]Robinson, P. L., ‘The exponential Weyl algebra’, University of Florida, preprint, 1988.Google Scholar
[7]Robinson, P. L., ‘Isomorphic exponential Weyl algebras’, Glasgow Math. J. 33 (1991), 7–10.CrossRefGoogle Scholar
[8]Slawny, J., ‘On factor representations and the C*-algebra of canonical commutation relations’, Comm. Math. Phys. 24 (1972), 151–170.CrossRefGoogle Scholar