Morphisms of relative Hopf modules, smash products, and duality
type: Item
instance of: scholarly article
title: Morphisms of relative Hopf modules, smash products, and duality
zbMATH Open document ID: 0937.16046
published in: Journal of Algebra
publication date: 2000-03-09T00:00:00Z
review text: Let \(H\) be a Hopf \(k\)-algebra, projective over \(k\), \(A\) a right \(H\)-comodule algebra and \({\mathcal M}_A^H\) the category of right \((H,A)\)-Hopf modules. The authors investigate the structure of the space of morphisms between objects of \({\mathcal M}_A^H\). The main result of this paper generalizes a theorem of \textit{H.-J.~Schneider} [in Advances in Hopf algebras, Lect. Notes Pure Appl. Math. 158, 267-297 (1994; Zbl 0817.16017)], obtained in the case when \(H\) is finite dimensional and \(A\) is an \(H\)-Galois extension of its coinvariants. Several duality theorems are obtained as corollaries, some of them extending known results, and a special attention is given to the case when \(H\) is co-Frobenius.
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 1346319
zbMATH Keywords: co-Frobenius Hopf algebras
zbMATH Keywords: Hopf Galois extensions
zbMATH Keywords: smash products
zbMATH Keywords: duality theorems
zbMATH Keywords: relative Hopf modules
zbMATH Keywords: endomorphism rings
zbMATH Keywords: comodule algebras
author: Claudia Menini
author: Serban Raianu
MaRDI profile type: Publication
OpenAlex ID: W2036432623
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DOI: 10.1006/JABR.1998.7842
description: scientific article; zbMATH DE number 1346319