EXPONENTIATIONS OVER THE QUANTUM ALGEBRA Uq(sl2(C))

We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra Uq(sl2(C)). We discuss two cases, according to whether the parameter q is a root of unity. We show that the universal enveloping algebra of sl2(C) embeds in a non-principal ultraproduct of Uq(sl2(C)), where q varies over the primitive roots of unity

Integrating Unitary Representations of Infinite-Dimensional Lie Groups

We show that in the presence of suitable commutator estimates, a projective unitary representation of the Lie algebra of a connected and simply connected Lie group G exponentiates to G. Our proof does not assume G to be finite--dimensional or of Banach-Lie type and therefore encompasses the diffeomorphism groups of compact manifolds. We obtain as corollaries short proofs of Goodman and Wallach's results on the integration of positive energy representations of loop groups and Diff(S^{1}) and of Nelson's criterion for the exponentiation of unitary representations of finite-dimensional Lie algebras.Comment: Available from Academic Press at http://www.academicpress.com/jf