{"title":"无限二面体群上的有限GK维Nichols代数","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":"{\"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}","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}
Finite GK-Dimensional Nichols Algebras Over the Infinite Dihedral Group
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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