Braiding structures of double crossproducts (Q1293143)

The aim of this paper is to study the braiding structures of double crossproducts. It is shown that for braided bialgebras \((X,\sigma)\) and \((A,\eta)\) and \(\nu,\nu'\in{\mathcal G}(X,A)\), then \((X\bowtie_\tau A,[\sigma,\eta,\nu,\nu'])\) is a braided bialgebra and any braiding of \(X\bowtie_\tau A\) has this form. Also, the author constructs several (braided) monoidal functors so as to discuss the relations between the comodule categories attached to double crossproducts. For \(H=X\bowtie_\tau A\) a double crossproduct by a fixed invertible skew pairing \(\tau\) on \(X\otimes A\), the monoidal functors \((F_X,\text{id}_k,\varphi_X)\) and \((F_A,\text{id}_k,\varphi_A)\) are obtained respectively from the monoidal category \(M^H\) to \(M^X\) and from \(M^H\) to \(M^A\); the braided monoidal functor \((G,\psi_0,\psi_2)\) is obtained from \(M^X\times M^A\) to \(M^H\).