Álgebra de Hopf trançada a partir de um par combinado de grupos

Abstract

Let (F,G, ◃, ▹) be a matched pair of finite groups and σ : F × F −→ (|×)G and τ : G×G −→ (|×)F two 2-cocycles. In general, the bicrossed product R = |G ∗τ σ |F is not a bialgebra, neither a braided Hopf algebra. The purpose of this work is to study necessary and sufficient conditions over σ, τ and a braid c such that R is a braided Hopf algebra in the category of Yetter-Drinfeld modules over some Hopf algebra H, in addition to present the cohomological interpretation of this result.