{"title":"完全互不相连的局部紧凑群在其边界上的作用的交叉积的简单性","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":"{\"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}","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}
Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries
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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