Tristan Bice, Lisa Orloff Clark, Ying-Fen Lin, Kathryn McCormick
{"title":"Cartan semigroups and twisted groupoid C*-algebras","authors":"Tristan Bice, Lisa Orloff Clark, Ying-Fen Lin, Kathryn McCormick","doi":"arxiv-2407.05024","DOIUrl":null,"url":null,"abstract":"We prove that twisted groupoid C*-algebras are characterised, up to\nisomorphism, by having Cartan semigroups, a natural generalisation of\nnormaliser semigroups of Cartan subalgebras. This extends the classic\nKumjian-Renault theory to general twisted \\'etale groupoid C*-algebras, even\nnon-reduced C*-algebras of non-effective groupoids.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"57 29 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-06","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-2407.05024","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
We prove that twisted groupoid C*-algebras are characterised, up to
isomorphism, by having Cartan semigroups, a natural generalisation of
normaliser semigroups of Cartan subalgebras. This extends the classic
Kumjian-Renault theory to general twisted \'etale groupoid C*-algebras, even
non-reduced C*-algebras of non-effective groupoids.
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