THE UNIVERSAL R-MATRIX FOR THE JORDANIAN DEFORMATION OF sl(2), AND THE CONTRACTED FORMS OF so(4)

Abstract

We introduce a universal R-matrix for the Jordanian deformation of U( sl (2)). Using Uh( so (4))=Uh( sl (2)) ⊕ U−h( sl (2)), we obtain the universal R-matrix for Uh( so (4)). Applying the graded contractions on the universal R-matrix of Uh( so (4)), we show that there exist three distinct R-matrices for all the contracted algebras. It is shown that Uh( sl (2)), Uh( so (4)), and all of these contracted algebras are triangular.