On pointed Hopf algebras over dihedral groups.
type: Item
instance of: scholarly article
title: On pointed Hopf algebras over dihedral groups.
zbMATH Open document ID: 1234.16020
author: Gastón Andrés García
author: Fernando Fantino
published in: Pacific Journal of Mathematics
publication date: 2011-11-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.0227
full work available at URL: p05.xhtml
review text: Let \(k\) be an algebraically closed field of characteristic zero and let \(D_m\) be the dihedral group of order \(2m\). In this paper the authors complete the classification of finite-dimensional Nichols algebras over \(D_m\), where \(m=4t\), \(t\geq 3\). Based on the so-called Lifting Method due to N. Andruskiewitsch and H.-J. Schneider, this allows in turn to give the classification of finite-dimensional pointed Hopf algebras over \(k\) with group of group-like elements isomorphic to \(D_m\). The proof of the main result on Nichols algebras uses the classification of finite-dimensional Nichols algebras of diagonal type, done by \textit{I. Heckenberger} [in Adv. Math. 220, No. 1, 59-124 (2009; Zbl 1176.17011)].
reviewed by: Sonia Natale
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 5980223
zbMATH Keywords: pointed Hopf algebras
zbMATH Keywords: Nichols algebras
zbMATH Keywords: dihedral groups
zbMATH Keywords: group-like elements
Wikidata QID: Q105627908
MaRDI profile type: Publication
OpenAlex ID: W2114367275
arXiv ID: 1007.0227
DOI: 10.2140/PJM.2011.252.69
description: scientific article