ON THE (CO)COMMUTATIVITY CLASS OF A HOPF ALGEBRA AND CROSSED PRODUCTS IN A BRAIDED CATEGORY

Abstract

In this paper, for two Hopf algebras A, H and a normal twisted cocycle σ in a braided monoidal category C we construct a Hopf algebra A _σ ⋊ H that generalizes the ones defined by S. Majid in 5-7. Moreover, we prove that recent constructions of crossed products of Hopf algebras in a category of modules over a field, for example, the Hopf algebra A ☆ H considered by Wang and Li in [10], are examples of the Majid constructions and then special cases of A _σ ⋊ H.

ACKNOWLEDGMENTS

The authors thank the referees for their interesting remarks. The authors has been supported by the Xunta de Galicia (Project: PGIDT00PXI20706PR).