THE BRAIDED STRUCTURES FOR T-SMASH PRODUCT HOPF ALGEBRAS

As a dual concept of quasitriangular bialgebra, braided bialgebras were introduced by Larson and Towber. The braided structures of omega-smash coproduct Hopf algebras have been investigated recently by the authors. Here we study the braided structures of T-smash product Hopf algebras B(SIC)(T)H as constructed by Caenepeel, Ion, Militaru and Zhu. Necessary and sufficient conditions for T-smash product Hopf algebras to be braided Hopf algebras are given in terms of properties of their components. We apply our results to discuss some special cases. In particular, braided structures of the Drinfeld double D(H) and of H-4(SIC)(T)RZ(2) = H-4 * RZ(2) (skew-group ring) are constructed.