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

Let π be a group and (H = {Hα}α∈π, μ, η) a Hopf π-algebra. First, we introduce the concept of quasitriangular Hopf π-algebra, and then prove that the left H-π-module category $_{H}\mathcal{M}$, where (H, R) is a quasitriangular Hopf π-algebra, is a braided monoidal category. Second, we give the construction of Hopf π-crossed coproduct algebra $C\natural_{\nu}^{\pi} H$. At last, the necessary and sufficient conditions for $C\natural_{\nu}^{\pi} H$ to be a quasitriangular Hopf π-algebra are derived, and in this case, ${}_{C\natural_{\nu}^{\pi} H}{\mathcal M}$ is a braided monoidal category.