A construction of braided Hopf algebras

Abstract

Under suitable assumption, we present a method to construct braided Hopf algebras (braided groups) $\bar{B}$ and $\underline{B}$ and in Yetter--Drinfel'd category ${}_H\mathscr{Y}\mathscr{D}^H_1$ and ${}_H\mathscr{Y}\mathscr{D}^H_2$ respectively. As applications, we study some special cases in both module and comodule form for $H$ quasitriangular and for $H$ coquasitriangular respectively. Finally, some examples are given.