Galois theory for multiplier Hopf algebras with integrals
type: Item
instance of: scholarly article
title: Galois theory for multiplier Hopf algebras with integrals
zbMATH Open document ID: 0929.16038
DOI: 10.1023/A:1009938708033
author: Yinhuo Zhang
author: Alfons Van Daele
published in: Algebras and Representation Theory
publication date: 1999-11-07T00:00:00Z
review text: A Hopf Galois theory is developed for regular multiplier Hopf algebras with integrals. The notion of a coaction of a multiplier Hopf algebra on an algebra is introduced, and a Morita context connecting the smash product and the coinvariants is constructed. As in the case of finite dimensional Hopf algebras studied by \textit{M. Cohen}, \textit{D. Fischman} and \textit{S. Montgomery} [in J. Algebra 133, No. 2, 351-372 (1990; Zbl 0706.16023)] and in the case of co-Frobenius Hopf algebras studied by \textit{M. Beattie}, \textit{S. Dăscălescu} and \textit{Ş. Raianu} [in J. Algebra 198, No. 1, 164-183 (1997; Zbl 0901.16017)], a Galois extension can be characterized by the surjectivity of a certain map in the Morita context. The results are applied to prove duality theorems for co-Frobenius Hopf algebras.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 1310751
zbMATH Keywords: multiplier Hopf algebras
zbMATH Keywords: integrals
zbMATH Keywords: Morita contexts
zbMATH Keywords: co-Frobenius Hopf algebras
zbMATH Keywords: Hopf Galois extensions
zbMATH Keywords: actions
zbMATH Keywords: coactions
zbMATH Keywords: smash products
zbMATH Keywords: coinvariants
reviewed by: Sorin Dascalescu
MaRDI profile type: Publication
full work available at URL: a:1009938708033
OpenAlex ID: W142111801
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description: scientific article; zbMATH DE number 1310751