The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4)

Details The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4) The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4)

1995-12-21

arxiv.org/abs/q-alg/9512022v1

Mathematics

Quantum Algebra

LaTeX, 8 pages

Scientific paper

10.1142/S0217732396000229

We introduce a universal R matrix for the Jordanian deformation of $\U{ \sl(2)}$. Using $\Uh{\so(4)}=\Uh{\sl(2)} \oplus {\rm U}_{-h}(\sl(2))$, 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 of the contracted algebras. It is shown that $\Uh{\sl(2)}$, $\Uh{\so(4)}$, and all of these contracted algebras are triangular.

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