On the coradical filtration of pointed coalgebras
type: Item
instance of: scholarly article
title: On the coradical filtration of pointed coalgebras
zbMATH Open document ID: 1022.16028
DOI: 10.1016/S0021-8693(02)00141-2
author: Darren B. Parker
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The author studies some aspects of the coradical filtration of pointed Hopf algebras. In particular, he proves a useful stronger version of the Taft-Wilson theorem. He then considers field extensions. He proves: If \(C\) is a cocommutative \(K\)-coalgebra and \(K\subseteq L\) is a field extension, then \(E\otimes C\) is pointed if and only if, for each simple subcoalgebra \(D\subseteq C\), \(E\) contains the normal closure of the field \(D^*\) over \(K\). He considers moreover the coradical filtration of duals of inseparable field extensions. The problem is reduced to the case that the extension \(K\subseteq L\) is purely inseparable and \(E\) is a field containing the normal closure of \(L\) over \(K\). Then it is proved that \(E\otimes L^*=(E\otimes L^*)_1\), if and only if \(L/K\) is separable of \(\text{char}(K)=2=[L:L_s]\), where \(L_s\) is the separable closure of \(K\) in \(L\).
reviewed by: Miriam Cohen
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W70
zbMATH DE Number: 1867994
zbMATH Keywords: coradical filtrations
zbMATH Keywords: pointed Hopf algebras
zbMATH Keywords: Taft-Wilson theorem
zbMATH Keywords: cocommutative coalgebras
zbMATH Keywords: simple subcoalgebra
zbMATH Keywords: inseparable field extensions
zbMATH Keywords: separable closures
MaRDI profile type: Publication
cites work: Q3933122
cites work: Q5328221
cites work: Biinvertible actions of Hopf algebras
cites work: Forms of coalgebras and Hopf algebras
cites work: On the structure of commutative pointed Hopf algebras
cites work: On the structure of pointed coalgebras
cites work: On antipodes in pointed Hopf algebras
description: scientific article; zbMATH DE number 1867994