Hopf algebras of dimension 12
type: Item
instance of: scholarly article
title: Hopf algebras of dimension 12
zbMATH Open document ID: 1020.16030
DOI: 10.1023/A:1020504123567
author: Sonia Natale
published in: Algebras and Representation Theory
publication date: 2003-03-10T00:00:00Z
review text: In this article, the author concludes the classification of Hopf algebras of dimension \(12\) over \(k\), an algebraically closed field of characteristic zero. Semisimple Hopf algebras of dimension \(12\) were classified by \textit{N. Fukuda} [in Tsukuba J. Math. 21, No. 1, 43-54 (1997; Zbl 0897.16021)]. The classification of pointed nonsemisimple Hopf algebras of dimension \(12\) follows from \textit{N. Andruskiewitsch} and \textit{S. Natale} [Tsukuba J. Math. 25, No. 1, 187-201 (2001; Zbl 0998.16026)]. The main result in this paper is that either \(H\) or \(H^*\) is pointed for a nonsemsimple Hopf algebra \(H\) of dimension \(12\) over \(k\). In view of this result and Andruskiewitsch and Natale's and Fukuda's conclusions, the full classification of Hopf algebras of dimension \(12\) over \(k\) follows.
reviewed by: Fang Li
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 1879214
zbMATH Keywords: finite-dimensional Hopf algebras
zbMATH Keywords: nonsemisimple Hopf algebras
zbMATH Keywords: pointed Hopf algebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879214