TOWARDS A GENERAL CONSTRUCTION OF NONSTANDARD R-H-MATRICES AS CONTRACTION LIMITS OF R-Q-MATRICES - THE U-H(SL(N)) ALGEBRA CASE

A class of transformations of R-q-matrices is introduced such that the q --> 1 limit gives explicit nonstandard R-h-matrices. The transforma tion matrix is singular as q --> 1. For the transformed matrix, the si ngularities, however, cancel yielding a well-defined construction. Our method can be implemented systematically on R-q-matrices of all dimen sions and not only for q-deformed sl(2) algebra but also for algebras of higher dimensions. Explicit constructions are presented starting wi th U-q(sl(2)) and U-q(sl(3)), while choosing R-q for (fund. rep.) x (a rbitrary irrep.). The treatment for the general case of U-q(sl(N)) alg ebras is indicated. Our method yields nonstandard deformations along w ith a nonlinear map of the h-Borel subalgebra on the corresponding cla ssical Borel subalgebra. For U-h(sl(2)) this map is extended to the wh ole algebra and compared with the other proposed by us previously. The usual classical coproduct on U(sl(2)) and the non-cocommutative copro duct structure on U-h(sl(2)) are related via Drinfeld twist operators, determined up to O(h(2)) for both of these nonlinear maps.