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A generalized Poisson bracket and an associated natural one-form

Published online by Cambridge University Press:  24 October 2008

A. Sudbery
A. Sudbery
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD
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Abstract

Starting from an arbitrary algebra in place of the algebra of smooth functions on a differentiable manifold M, we construct an algebra which generalizes the algebra of polynomial functions on T*M. We define a Poisson bracket on this algebra and show that it can be obtained from a natural one-form which generalizes the fundamental one-form on T*M.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 1 , January 1977 , pp. 133 - 142
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Bloore, F. J. and Assimakopoulos, M.A natural one-form for the Schouten concomitant. Liverpool University preprint (07 1975).Google Scholar
(2)Hermann, R.Geometry, physics and systems (New York, Dekker, 1973), p. 42.Google Scholar