{"title":"实数域上重复代数的表示类型","authors":"Mengdie Zhang, Chaowen Zhang","doi":"10.1142/s1005386723000251","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be a finite-dimensional algebra over the real number field. We prove that the repetitive algebra [Formula: see text] admits the dichotomy property of representation type, i.e., [Formula: see text] is either of discrete representation type or of strongly unbounded type.","PeriodicalId":50958,"journal":{"name":"Algebra Colloquium","volume":"10 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Representation Type of Repetitive Algebras over the Real Number Field\",\"authors\":\"Mengdie Zhang, Chaowen Zhang\",\"doi\":\"10.1142/s1005386723000251\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let [Formula: see text] be a finite-dimensional algebra over the real number field. We prove that the repetitive algebra [Formula: see text] admits the dichotomy property of representation type, i.e., [Formula: see text] is either of discrete representation type or of strongly unbounded type.\",\"PeriodicalId\":50958,\"journal\":{\"name\":\"Algebra Colloquium\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Colloquium\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1005386723000251\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Colloquium","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386723000251","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Representation Type of Repetitive Algebras over the Real Number Field
Let [Formula: see text] be a finite-dimensional algebra over the real number field. We prove that the repetitive algebra [Formula: see text] admits the dichotomy property of representation type, i.e., [Formula: see text] is either of discrete representation type or of strongly unbounded type.
期刊介绍：
Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.
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