Basic Hopf algebras of tame type.
type: Item
instance of: scholarly article
title: Basic Hopf algebras of tame type.
zbMATH Open document ID: 1285.16028
author: Liu Gongxiang
published in: Algebras and Representation Theory
publication date: 2013-06-13T00:00:00Z
review text: The classification of all finite-dimensional basic Hopf algebras of tame type over an algebraically closed field of characteristic 0 is given. This is a continuation of the articles [\textit{G. Liu}, J. Algebra 299, No. 2, 841-853 (2006; Zbl 1110.16045); \textit{H.-L. Huang} and \textit{G. Liu}, J. Algebra 321, No. 9, 2650-2669 (2009; Zbl 1173.16018)], where classification of all radically graded basic Hopf algebras of tame type and classification of basic Hopf algebras of finite representation type were given, respectively. As a consequence it is proved that the representation dimension of a tame basic Hopf algebra is exactly \(3\). Moreover, the author shows that for a basic Hopf algebra \(H\), if \(C(H)\geq 3\) then it is wild, where \(C(H)\) is the complexity of \(H\). The last corollary is connected with Rickard's conjecture and statement about complexity of modules over self-injective tame algebras.
reviewed by: Justyna Kosakowska
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16G60
zbMATH DE Number: 6175492
zbMATH Keywords: finite-dimensional basic Hopf algebras
zbMATH Keywords: representation types
zbMATH Keywords: representation dimension
zbMATH Keywords: complexities of modules
MaRDI profile type: Publication
full work available at URL: s10468-011-9331-1
OpenAlex ID: W1976542843
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DOI: 10.1007/S10468-011-9331-1
description: scientific article; zbMATH DE number 6175492