{"title":"Pointwise inner automorphisms of almost periodic factors","authors":"Cyril Houdayer, Yusuke Isono","doi":"10.1007/s00029-024-00949-z","DOIUrl":null,"url":null,"abstract":"<p>We prove that a large class of nonamenable almost periodic type III<span>\\(_1\\)</span> factors <i>M</i>, including all McDuff factors that tensorially absorb <span>\\(R_\\infty \\)</span> and all free Araki–Woods factors, satisfy Haagerup–Størmer’s conjecture (1988): any pointwise inner automorphism of <i>M</i> is the composition of an inner and a modular automorphism.</p>","PeriodicalId":501600,"journal":{"name":"Selecta Mathematica","volume":"352 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Selecta Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00029-024-00949-z","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 a large class of nonamenable almost periodic type III\(_1\) factors M, including all McDuff factors that tensorially absorb \(R_\infty \) and all free Araki–Woods factors, satisfy Haagerup–Størmer’s conjecture (1988): any pointwise inner automorphism of M is the composition of an inner and a modular automorphism.
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