The structure theorem for comodule algebras over Hopf algebroids.
type: Item
instance of: scholarly article
title: The structure theorem for comodule algebras over Hopf algebroids.
zbMATH Open document ID: 1235.16030
author: Liangyun Zhang
author: Y. H. Wang
published in: Acta Mathematica Hungarica
publication date: 2012-02-14T00:00:00Z
review text: \textit{G. Militaru} and \textit{D. Stefan} [Commun. Algebra 22, No. 14, 5657-5678 (1994; Zbl 0816.16029)] showed that comodule algebras over Hopf algebras are smash products if and only if there exists a comodule algebra morphism from the Hopf algebra to the comodule algebra. Later this was generalized to comodule algebras over quasi-Hopf algebras [\textit{F. Panaite} and \textit{F. Van Oystaeyen}, Proc. Am. Math. Soc. 135, No. 6, 1669-1677 (2007; Zbl 1160.16021)]. The goal of the paper under review is to generalize this even further to comodule algebras over Hopf algebroids. The main tool is a structure theorem for \((H,\mathcal H)\)-Hopf bimodules, where \(\mathcal H\) is a Hopf algebroid on the total Hopf algebra \(H\).
reviewed by: Jörg Feldvoss
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16T15
Mathematics Subject Classification ID: 16S40
zbMATH DE Number: 6006424
zbMATH Keywords: Hopf algebroids
zbMATH Keywords: Hopf bimodules
zbMATH Keywords: comodule algebras
zbMATH Keywords: smash products
zbMATH Keywords: structure theorem
MaRDI profile type: Publication
full work available at URL: s10474-011-0084-4
OpenAlex ID: W2093551390
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DOI: 10.1007/S10474-011-0084-4
description: scientific article; zbMATH DE number 6006424