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

Abstract

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 [Formula: see text], 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 [Formula: see text]. At last, the necessary and sufficient conditions for [Formula: see text] to be a quasitriangular Hopf π-algebra are derived, and in this case, [Formula: see text] is a braided monoidal category.