In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of such that * for all , where is the coproduct on H, and the linear map is given by , * , * , where , , and , where , , and , are algebra morphisms determined by R is called the R-matrix. It is possible to construct a quasitriangular Hopf algebra from a Hopf algebra and its dual, using the Drinfeld quantum double construction. If the Hopf algebra H is quasitriangular, then the category of modules over H is braided with braiding .