TOWARDS A GENERAL CONSTRUCTION OF NONSTANDARD Rh-MATRICES AS CONTRACTION LIMITS OF Rq-MATRICES: THE ${\mathcal U}_h ({\rm sl}(N))$ ALGEBRA CASE

Abstract

A class of transformations of Rq-matrices is introduced such that the q→1 limit gives explicit nonstandard Rh-matrices. The transformation matrix is singular as q→1. For the transformed matrix, the singularities, however, cancel yielding a well-defined construction. Our method can be implemented systematically on Rq-matrices of all dimensions and not only for q-deformed sl(2) algebra but also for algebras of higher dimensions. Explicit constructions are presented starting with [Formula: see text] and [Formula: see text], while choosing Rq for (fund. rep.) ⊗ (arbitrary irresp.). The treatment for the general case of [Formula: see text] algebras is indicated. Our method yields nonstandard deformations along with a nonlinear map of the h-Borel subalgebra on the corresponding classical Borel subalgebra. For [Formula: see text] this map is extended to the whole algebra and compared with the other proposed by us previously. The usual classical coproduct on [Formula: see text] and the non-cocommutative coproduct structure on [Formula: see text] are related via Drinfeld twist operators, determined up to O(h2) for both of these nonlinear maps.