A description of the embedding of a centrally extended Askey–Wilson algebra, AW(3), in Uq(sl2) 3 is given in terms of the universal R-matrix of Uq(sl2). The generators of the centralizer of Uq(sl2) 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 AW(3) under the embedding map by showing that they obey the AW(3) relations. This is achieved by introducing a natural coaction also constructed with the help of the R-matrix.