A class of braided monoidal categories via quasitriangular Hopf π-crossed coproduct algebras

Let pi be a group and (H = {H-alpha} alpha is an element of pi, mu, eta) a Hopf pi-algebra. First, we introduce the concept of quasitriangular Hopf pi-algebra, and then prove that the left H-p-module category M-H, where (H, R) is a quasitriangular Hopf pi-algebra, is a braided monoidal category. Second, we give the construction of Hopf pi-crossed coproduct algebra C-nu(pi). H. At last, the necessary and sufficient conditions for C-nu(pi). H to be a quasitriangular Hopf pi-algebra are derived, and in this case, C-nu(pi). HM is a braided monoidal category.