{"title":"Structure of Relatively Biexact Group von Neumann Algebras","authors":"Changying Ding, Srivatsav Kunnawalkam Elayavalli","doi":"10.1007/s00220-024-04987-8","DOIUrl":null,"url":null,"abstract":"<p>Using computations in the bidual of <span>\\({\\mathbb {B}}(L^2M)\\)</span> we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of <span>\\(L\\Gamma \\)</span> where <span>\\(\\Gamma \\)</span> is an infinite group that is biexact relative to a finite family of subgroups <span>\\(\\{\\Lambda _i\\}_{i\\in I}\\)</span> such that each <span>\\(\\Lambda _i\\)</span> is almost malnormal in <span>\\(\\Gamma \\)</span>. This generalizes the result of Ding et al. (Properly proximal von Neumann algebras, 2022. arXiv:2204.00517) which classifies subalgebras of von Neumann algebras of biexact groups. By developing a combination with techniques from Popa’s deformation-rigidity theory we obtain a new structural absorption theorem for free products and a generalized Kurosh type theorem in the setting of properly proximal von Neumann algebras.\n</p>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s00220-024-04987-8","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Using computations in the bidual of \({\mathbb {B}}(L^2M)\) we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of \(L\Gamma \) where \(\Gamma \) is an infinite group that is biexact relative to a finite family of subgroups \(\{\Lambda _i\}_{i\in I}\) such that each \(\Lambda _i\) is almost malnormal in \(\Gamma \). This generalizes the result of Ding et al. (Properly proximal von Neumann algebras, 2022. arXiv:2204.00517) which classifies subalgebras of von Neumann algebras of biexact groups. By developing a combination with techniques from Popa’s deformation-rigidity theory we obtain a new structural absorption theorem for free products and a generalized Kurosh type theorem in the setting of properly proximal von Neumann algebras.
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.