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