The universal dual comodule of module in Hopf algebras.
type: Item
instance of: scholarly article
title: The universal dual comodule of module in Hopf algebras.
zbMATH Open document ID: 1042.16025
DOI: 10.1016/S0252-9602(17)30334-X
author: Zhifeng Hao
author: Liangui Feng
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2003-10-29T00:00:00Z
review text: Given an algebra \(A\) over a field \(k\), the vector space \(A^0\) of all linear forms \(f\in A^*\) such that the cyclic left \(A\)-module \(Af\) is finite dimensional over \(k\) is known to be a coalgebra. The authors consider an analogous construction \(M^0\) of a right \(A^0\)-comodule for each right \(A\)-module \(M\). The main result (Theorem 4) gives the formula \((M\otimes_A N)^0\cong M^0\square_{A^0}N^0\) for modules \(M,N\) over a commutative algebra \(A\), which relates tensor and cotensor products. However, the second line of its proof reveals a conceptual misunderstanding of the nature of tensor product which sheds some doubts on the validity of this theorem.
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 1997646
zbMATH Keywords: universal dual comodules
zbMATH Keywords: Hopf algebras
zbMATH Keywords: cotensor products
zbMATH Keywords: adjoint functors
reviewed by: José Gómez-Torrecillas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1997646