CHAOS MAP FOR THE UNIVERSAL ENVELOPING ALGEBRA OF U(N)

It is shown that the family of representations {j(t), t is an element of R(+)} of the universal enveloping algebra U of the N-dimensional un itary group which is generated by the N-dimensional number process of quantum stochastic calculus can be expressed in the form j(t) = I(t)o psi, where psi is a bijective linear map from U onto the space L of sy mmetric tensors over the Lie algebra, and I-t is the iterated (chaotic ) integral on L. The chaotic product is defined by the formula psi(L M) = psi(L)psi(M) and satisfies I-t(S*T) = I-t(S)I-t(T). This work ge neralizes and completes earlier results on the centre of U.