Examples of equivalences of Doi-Koppinen Hopf module categories, including Yetter-Drinfeld modules
type: Item
instance of: scholarly article
title: Examples of equivalences of Doi-Koppinen Hopf module categories, including Yetter-Drinfeld modules
zbMATH Open document ID: 0926.16033
author: Peter Schauenburg
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1999-03-15T00:00:00Z
review text: Let \(H\) be a Hopf algebra and \(^H_H{\mathcal M}^H_H\) the category of two-sided two-cosided Hopf modules in the sense of Woronowicz. Then there exists a Doi-Hopf datum \((A,B,D)\) such that the above category is equivalent to the category of Hopf modules in the sense of Doi-Koppinen \(^D_B{\mathcal M}(A)\). This implies a category equivalence between the category of two-sided two-cosided Hopf modules and the category \(^H_H\mathcal{YD}\) of Yetter-Drinfeld (or crossed) modules.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 1260637
zbMATH Keywords: Yetter-Drinfeld modules
zbMATH Keywords: Hopf algebras
zbMATH Keywords: categories of Hopf modules
zbMATH Keywords: category equivalences
reviewed by: Serban Raianu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1260637