Survey of braided Hopf algebras (Q2708922)

A braided Hopf algebra [\textit{S. Majid}, Lect. Notes Pure Appl. Math. 158, 55-105 (1994; Zbl 0812.18004)] is a Hopf algebra object in a braided tensor category. The main aim of this paper is to define and study braided Hopf algebras without using braided tensor categories. Thus, the author defines a braided bialgebra as a bialgebra with a Yang-Baxter operator which satisfies some compatibility conditions. The main result of the paper states that a Yetter-Drinfeld bialgebra (a bialgebra in the braided category of Yetter-Drinfeld modules), is a braided bialgebra and conversely, an arbitrary rigid braided bialgebra can be realized as a Yetter-Drinfeld bialgebra. In the last section the author presents recent results on finite dimensional Yetter-Drinfeld Hopf algebras from his new point of view.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00038].