Braided Hopf algebras arising from matched pairs of groups

Let be a field. Let also (F,G) be a matched pair of groups. We give necessary and sufficient conditions on a pair (σ,τ) of 2-cocycles in order that the crossed product algebra and the crossed coproductcoalgebra combine into a braided Hopf algebra. We also discuss diagonal realizations of such braided Hopf algebras in the category of Yetter–Drinfeld modules over a finite group.