The braided structures for ω-smash coproduct Hopf algebras

Braided bialgebras were introduced by Larson and Towber by considering a bilinear form with certain properties. Here we study the braided structures of ω-smash coproduct Hopf algebras Bω H as constructed by Caenepeel, Ion, Militaru and Zhu. Necessary and sufficient conditions for a class of ω-smash coproduct Hopf algebras to be braided Hopf algebras are given in terms of properties of their components. As applications of our results some special cases are discussed and explicit examples are given.