{"title":"Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries","authors":"Ryoya Arimoto","doi":"10.1016/j.jfa.2024.110732","DOIUrl":null,"url":null,"abstract":"<div><div>We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial converse of this result.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110732"},"PeriodicalIF":1.7000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123624004208","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial converse of this result.
期刊介绍：
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis
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