{"title":"Weyl groups of groupoid C*-algebras","authors":"Fuyuta Komura","doi":"arxiv-2409.04906","DOIUrl":null,"url":null,"abstract":"In the theory of C*-algebras, the Weyl groups were defined for the Cuntz\nalgebras and graph algebras by Cuntz and Conti et.al respectively. In this\npaper, we introduce and investigate the Weyl groups of groupoid C*-algebras as\na natural generalization of the existing Weyl groups. Then we analyse several\ngroups of automorphisms on groupoid C*-algebras. Finally, we apply our results\nto Cuntz algebras, graph algebras and C*-algebras associated with\nDeaconu-Renault systems.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04906","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
In the theory of C*-algebras, the Weyl groups were defined for the Cuntz
algebras and graph algebras by Cuntz and Conti et.al respectively. In this
paper, we introduce and investigate the Weyl groups of groupoid C*-algebras as
a natural generalization of the existing Weyl groups. Then we analyse several
groups of automorphisms on groupoid C*-algebras. Finally, we apply our results
to Cuntz algebras, graph algebras and C*-algebras associated with
Deaconu-Renault systems.
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