Theory of braided Hopf crossed products (Q1868917)

Let \(H\) be a braided bialgebra in the sense of \textit{M. Takeuchi} [Contemp. Math. 267, 301-323 (2000; Zbl 0978.16035)]. The authors propose a generalization of the classical concepts of smash product, crossed product, \(H\)-comodule algebra, \(H\)-module algebra, which extend their previous work [Contemp. Math. 267, 135-160 (2000; Zbl 0976.16023)]. It is explained how many results for usual crossed products remain valid in this generalized situation. Among them we mention the existence of a Morita context connecting the smash product \(A\#H\) and the ring of invariants \(A^H\) for the action of a rigid braided Hopf algebra \(H\) on an algebra \(A\), a Maschke theorem for the generalized crossed product over a semisimple braided Hopf algebra, and the description of equivalent crossed products.