Quasitriangular structures of bicrossed coproducts (Q1270964)

Let \(H\) and \(A\) be two bialgebras (Hopf algebras) coacting on each other. The tensor product \(H\otimes A\) is endowed with a bialgebra (Hopf algebra) structure, called the bicrossed coproduct of \(H\) and \(A\). An example is the dual of the Drinfeld double of a Hopf algebra. The aim of the paper is to show that the bicrossed coproduct is a quasitriangular bialgebra if and only if so are \(H\) and \(A\). Moreover, all quasitriangular structures of the bicrossed coproduct are described in terms of the ones of \(H\) and \(A\).