On the classification of strongly graded Hopf algebras
type: Item
instance of: scholarly article
title: On the classification of strongly graded Hopf algebras
zbMATH Open document ID: 1020.16024
published in: Journal of Algebra
publication date: 2002-09-08T00:00:00Z
review text: The author studies strong \(G\)-graded bialgebra extensions \(S\) of a bialgebra \(R\). He shows how to extend an antipode of \(R\) to an antipode of \(S\) compatible with the grading. He then investigates the set \(\text{Ext}_k(G,R)\) of isomorphism classes of such Hopf algebras \(S\) and shows \(\text{Ext}_\wp(G,R)\cong H^2_\wp(G,Z(R)^*)\) if the Teichmüller obstruction of the collective character \(\wp\colon G\to\text{Pic}_k(R)\) vanishes. Here \(Z(R)^*\) is the group of all central group-like elements of \(R\).
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 1797477
zbMATH Keywords: strongly graded Hopf algebras
zbMATH Keywords: extensions of bialgebras
zbMATH Keywords: group cohomology
zbMATH Keywords: Teichmüller obstruction
zbMATH Keywords: antipodes
zbMATH Keywords: group-like elements
author: Antonio M. Cegarra
reviewed by: Bodo Pareigis
MaRDI profile type: Publication
full work available at URL: jabr.2001.9125
OpenAlex ID: W2055592612
cites work: Q5562621
cites work: Graded extensions of monoidal categories
cites work: Group-graded rings and modules
cites work: Braided tensor categories
cites work: Q4693151
cites work: Q4857364
cites work: Biinvertible actions of Hopf algebras
cites work: Categories tannakiennes
DOI: 10.1006/JABR.2001.9125
description: scientific article; zbMATH DE number 1797477