Revisiting the Askey–Wilson algebra with the universal R-matrix of $\boldsymbol{ \newcommand{\su}{\mathfrak{sl}} U_q(\su_2)}$

A description of the embedding of a centrally extended Askey–Wilson algebra, , in is given in terms of the universal R-matrix of . The generators of the centralizer of in its three-fold tensor product are naturally expressed through conjugations of Casimir elements with R. They are seen as the images of the generators of under the embedding map by showing that they obey the relations. This is achieved by introducing a natural coaction also constructed with the help of the R-matrix.