{"title":"驯服型基本霍普夫代数的表示","authors":"Shiyu Lin, Shilin Yang","doi":"10.1007/s41980-024-00908-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, all string modules of one class of basic Hopf algebras of tame type, which are denoted by <span>\\(\\mathbb {H}_2\\)</span> are studied. Firstly, the isomorphism classes of all string modules of <span>\\(\\mathbb {H}_2\\)</span> are classified. Then the projective class ring of <span>\\(\\mathbb {H}_2\\)</span> is described. Finally, the McKay matrix and the corresponding McKay quiver of <span>\\(\\mathbb {H}_2\\)</span> are discussed.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Representations of Basic Hopf Algebras of Tame Type\",\"authors\":\"Shiyu Lin, Shilin Yang\",\"doi\":\"10.1007/s41980-024-00908-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, all string modules of one class of basic Hopf algebras of tame type, which are denoted by <span>\\\\(\\\\mathbb {H}_2\\\\)</span> are studied. Firstly, the isomorphism classes of all string modules of <span>\\\\(\\\\mathbb {H}_2\\\\)</span> are classified. Then the projective class ring of <span>\\\\(\\\\mathbb {H}_2\\\\)</span> is described. Finally, the McKay matrix and the corresponding McKay quiver of <span>\\\\(\\\\mathbb {H}_2\\\\)</span> are discussed.</p>\",\"PeriodicalId\":9395,\"journal\":{\"name\":\"Bulletin of The Iranian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Iranian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s41980-024-00908-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-024-00908-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Representations of Basic Hopf Algebras of Tame Type
In this paper, all string modules of one class of basic Hopf algebras of tame type, which are denoted by \(\mathbb {H}_2\) are studied. Firstly, the isomorphism classes of all string modules of \(\mathbb {H}_2\) are classified. Then the projective class ring of \(\mathbb {H}_2\) is described. Finally, the McKay matrix and the corresponding McKay quiver of \(\mathbb {H}_2\) are discussed.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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