Quasitriangular Hopf group algebras and braided monoidal categories

摘要

Let pi be a group, and H be a semi-Hopf pi-algebra. We first show that the category (H) M of left pi-modules over H is a monoidal category with a suitably defined tensor product and each element alpha in pi induces a strict monoidal functor from (H) M to itself. Then we introduce the concept of quasitriangular semi-Hopf pi-algebra, and show that a semi-Hopf pi-algebra H is quasitriangular if and only if the category (H) Mis a braided monoidal category and is a strict braided monoidal functor for any alpha a pi. Finally, we give two examples of Hopf pi-algebras and describe the categories of modules over them.