Monoidal functors on the category of representations of a triangular Hopf algebra
type: Item
instance of: scholarly article
title: Monoidal functors on the category of representations of a triangular Hopf algebra
zbMATH Open document ID: 0907.16020
DOI: 10.1007/BF02897439
published in: Science in China. Series A
publication date: 1998-12-15T00:00:00Z
review text: The author gives constructions of monoidal functors in braided monoidal categories related to quantum groups, i.e. related to quasitriangular Hopf algebras or braided Hopf algebras. He constructs for a given triangular Hopf algebra \((H,R)\) and for any \(H\)-module \(M\) with an integral \(e\) a universal quantum commutative algebra \(S^e_R(M)\), and obtains the tensor isomorphism theorem on the universal quantum commutative algebras. Based on this, he gives the construction of the dual \(M^o\) of an \(H\)-module \(M\) with integral, and it turns out that \(M^o\) is an \(H^o\)-comodule. Also, he obtains the tensor isomorphism theorem on the dual comodules.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 18D10
zbMATH DE Number: 1180421
zbMATH Keywords: quasitriangular Hopf algebras
zbMATH Keywords: braided monoidal categories
zbMATH Keywords: braided Hopf algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: monoidal functors
zbMATH Keywords: universal quantum commutative algebras
zbMATH Keywords: tensor isomorphism theorem
author: D.-M. Lu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1180421