{"title":"Classification results for\nnonsingular Bernoulli crossed products","authors":"S. Vaes, Bram Verjans","doi":"10.4064/sm220217-11-5","DOIUrl":null,"url":null,"abstract":"We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $\\tau$-invariant. These are the first such classification results beyond the well studied probability measure preserving case.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm220217-11-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $\tau$-invariant. These are the first such classification results beyond the well studied probability measure preserving case.
期刊介绍：
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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