{"title":"Finite GK-Dimensional Nichols Algebras Over the Infinite Dihedral Group","authors":"Yongliang Zhang","doi":"10.1007/s10468-023-10213-1","DOIUrl":null,"url":null,"abstract":"<div><p>We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GK-dimension for short, through the study of Nichols algebras over <span>\\(\\mathbb {D}_{\\infty }\\)</span>, the infinite dihedral group.We find all the irreducible Yetter-Drinfeld modules <i>V</i> over <span>\\(\\mathbb {D}_{\\infty }\\)</span>, and determine which Nichols algebras <span>\\(\\mathcal {B}(V)\\)</span> of <i>V</i> are finite GK-dimensional.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"161 - 177"},"PeriodicalIF":0.5000,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-023-10213-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GK-dimension for short, through the study of Nichols algebras over \(\mathbb {D}_{\infty }\), the infinite dihedral group.We find all the irreducible Yetter-Drinfeld modules V over \(\mathbb {D}_{\infty }\), and determine which Nichols algebras \(\mathcal {B}(V)\) of V are finite GK-dimensional.
期刊介绍：
Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups.
The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.
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