{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-023-10213-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.
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