Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T01:03:25.292Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of exponential Weyl algebras

Part of: Modules, bimodules and ideals Rings and algebras arising under various constructions 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
Rights & Permissions [Opens in a new window]

Abstract

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.

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