Theory of braided Hopf crossed products
type: Item
instance of: scholarly article
title: Theory of braided Hopf crossed products
zbMATH Open document ID: 1017.16032
DOI: 10.1016/S0021-8693(02)00546-X
published in: Journal of Algebra
publication date: 2003-04-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 16W22
zbMATH DE Number: 1901956
zbMATH Keywords: braided Hopf algebras
zbMATH Keywords: crossed products
zbMATH Keywords: smash products
zbMATH Keywords: Morita contexts
zbMATH Keywords: Maschke theorem
zbMATH Keywords: braided bialgebras
zbMATH Keywords: rings of invariants
author: Jorge A. Guccione
author: Juan J. Guccione
reviewed by: Sorin Dascalescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1901956