{"title":"Classification conjectures for Leavitt path algebras","authors":"Guillermo Cortiñas, Roozbeh Hazrat","doi":"10.1112/blms.13139","DOIUrl":null,"url":null,"abstract":"<p>The theory of Leavitt path algebras is intrinsically related, via graphs, to the theory of symbolic dynamics and <span></span><math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mo>∗</mo>\n </msup>\n <annotation>$C^*$</annotation>\n </semantics></math>-algebras where the major classification programs have been a domain of intense research in the last 50 years. In this article, we gather together current lines of research in the classification of Leavitt path algebras, questions, conjectures, and some of the results about them that have been obtained so far.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 10","pages":"3011-3060"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13139","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13139","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The theory of Leavitt path algebras is intrinsically related, via graphs, to the theory of symbolic dynamics and -algebras where the major classification programs have been a domain of intense research in the last 50 years. In this article, we gather together current lines of research in the classification of Leavitt path algebras, questions, conjectures, and some of the results about them that have been obtained so far.
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