It looks like your question was already answered, but I highly recommend the book by Klymik and Schüdgen for this sort of question. In particular, they spell out the formula for a ribbon element in a QUE's quite explicitly as I recall. Both an advantage and a drawback of that book are that they do everything very explicitly with formulas.

I could be wrong (don't have a text with me) but I thought that the formula was a slight modification of what Noah wrote: namely one takes as a first guess u=\mu(R_21 R_12), i.e. you take the two components of the squared R-matrix and multiply them. This is almost a ribbon element; it satifies a coproduct relation similar to the ribbon element, and more precisely, uS(u) is the square of the actual ribbon element. Thus, u has it be corrected by the factor Noah mentioned, e^{-h\rho}. In the end, I believe the ribbon element is e^{-h rho}u.

It looks like your question was already answered, but I highly recommend the book by Klymik and Schüdgen for this sort of question. In particular, they spell out the formula for a ribbon element in a QUE's quite explicitly as I recall. Both an advantage and a drawback of that book are that they do everything very explicitly with formulas.

I could be wrong (don't have a text with me) but I thought that the formula was a slight modification of what Noah wrote: namely one takes as a first guess u=\mu(R_21 R_12), i.e. you take the two components of the squared R-matrix and multiply them. This is almost a ribbon element; it satifies a coproduct relation similar to the ribbon element, and more precisely, uS(u) is the square of the actual ribbon element. Thus, u has to be corrected by the factor Noah mentioned, e^{-h\rho}. In the end, I believe the ribbon element is e^{-h rho}u.