A METHOD OF CONSTRUCTING

Let A and B be two Hopf algebras and R 2 Hom(B › A;A › B), the twisted tensor product Hopf algebra A#RB was introduced by S. Caenepeel et al in [3] and further studied in our recent work [6]. In this paper we give the necessary and su‐cient conditions for A#RB to be a Hopf algebra with a projection. Furthermore, a braided Hopf algebra A is constructed by twisting the multiplication of A through a (∞;R)-pair (A;B). Finally we give a method to construct Radford’s biproduct directly by deflning the module action and comodule action from the twisted tensor biproduct.