Twisted tensor coproduct of multiplier Hopf algebras.
type: Item
instance of: scholarly article
title: Twisted tensor coproduct of multiplier Hopf algebras.
zbMATH Open document ID: 1071.16032
published in: Journal of Algebra
publication date: 2004-10-01T00:00:00Z
review text: Let \(A\) and \(B\) be multiplier Hopf algebras, and let \(T\) be a cotwisting map, i.e. \(T\colon A\otimes B\to B\otimes A\) is an algebra isomorphism satisfying certain conditions. The author defines a comultiplication on the tensor product of algebras \(A\otimes B\) making it a multiplier Hopf algebra, called a twisted tensor coproduct. Skew copairings are introduced for multiplier Hopf algebras, and a cotwisting map is associated to any skew copairing. If \(A\) is an algebraic quantum group, i.e. a regular multiplier Hopf algebra with non-zero integrals, let \(\widehat A\) be the dual algebraic quantum group and \(D=\widehat A\times A^{cop}\) be the associated Drinfeld double, which is also an algebraic quantum group. The dual algebraic quantum group \(\widehat D\) is characterized as a twisted tensor coproduct.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W35
zbMATH DE Number: 2105373
zbMATH Keywords: multiplier Hopf algebras
zbMATH Keywords: algebraic quantum groups
zbMATH Keywords: cotwistings
zbMATH Keywords: Drinfeld doubles
zbMATH Keywords: copairings
zbMATH Keywords: integrals
zbMATH Keywords: comultiplications
zbMATH Keywords: tensor products
author: L. Delvaux
reviewed by: Sorin Dascalescu
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.09.006
OpenAlex ID: W2095095237
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DOI: 10.1016/J.JALGEBRA.2003.09.006
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description: scientific article; zbMATH DE number 2105373