Survey of cross product bialgebras (Q2762032)

The authors review recent developments in construction and classification of cross product bialgebras. Many of these developments are due to the authors of the article. First, the universal construction of cross product bialgebras is presented. This construction involves both cocycles and dual cocycles and generalises and unifies all the constructions known so far. Second, the crossed products related to a Hopf datum are discussed. These general constructions are then applied to show that a double biproduct Hopf algebra of \textit{S. Majid} [Math. Proc. Camb. Philos. Soc. 125, No. 1, 151-192 (1999; Zbl 0974.17018)] is a cross product in the braided category of Hopf bimodules.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00024].