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Chaos map for the universal enveloping algebra of U(N)*

Published online by Cambridge University Press:  24 October 2008

R. L. Hudson  and
K. R. Parthasarathy
R. L. Hudson
Affiliation:
Mathematics Department, University of Nottingham, Nottingham NG7 2RD
K. R. Parthasarathy
Affiliation:
Mathematics Department, University of Nottingham, Nottingham NG7 2RD
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Abstract

It is shown that the family of representations {jt, t ∈ ℝ+} of the universal enveloping algebra U of the N-dimensional unitary group which is generated by the N-dimensional number process of quantum stochastic calculus can be expressed in the form

where ψ is a bijective linear map from U onto the space S of symmetric tensors over the Lie algebra, and It is the iterated (chaotic) integral on S. The chaotic product * is defined by the formula

and satisfies

This work generalizes and completes earlier results on the centre of U.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 21 - 30
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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