ADDITION OF INDEPENDENT VARIABLES IN QUANTUM GROUPS

A q-analog version of the quantum central limit theorem (qclt) for qua ntum groups U(q)(q) with generators {e(i), f(i), t(i), t(i)-1}1 less-t han-or-equal-to i less-than-or-equal-to n and associated bialgebras C (subject to CR1 t(i)t(i)-1 = t(i)-1t(i), t(i)t(j) = t(j)t(i)) and C(q) (subject to CRI and CR2: t(i)e(j) = q(a)(ij)e(j)t(i), t(i)f(j) = q(-a )(ij)f(j)t(i) is presented. Our approach is based on the method of mom ents of Giri and von Waldenfels [6] and von Waldenfels [18] for tensor ungraded and graded algebras, respectively. Thus, it is shown that fo r certain functionals phi, one can evaluate the limit of moments phi(N )(v1N...v(p)N), where v(i)N are generators subject to some CR with the normalization related to [N], the q-analog of N, phi(N) = phi x N) = circle DELTA(N-1), where DELTA is the coproduct in C and DELTA(N) its Nth iteration. This work is restricted to q is-an-element-of R+.