{"title":"交换平方与平面子代数","authors":"Keshab Chandra Bakshi, Vijay Kodiyalam","doi":"10.7900/jot.2020feb06.2279","DOIUrl":null,"url":null,"abstract":"We show a close relationship between non-degenerate smooth commuting squares of II1-factors with horizontal inclusions of finite index and inclusions of subfactor planar algebras by showing that each leads to a construction of the other. One direction of this uses the Guionnet--Jones--Shlyakhtenko construction.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Commuting squares and planar subalgebras\",\"authors\":\"Keshab Chandra Bakshi, Vijay Kodiyalam\",\"doi\":\"10.7900/jot.2020feb06.2279\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show a close relationship between non-degenerate smooth commuting squares of II1-factors with horizontal inclusions of finite index and inclusions of subfactor planar algebras by showing that each leads to a construction of the other. One direction of this uses the Guionnet--Jones--Shlyakhtenko construction.\",\"PeriodicalId\":50104,\"journal\":{\"name\":\"Journal of Operator Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2019-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7900/jot.2020feb06.2279\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7900/jot.2020feb06.2279","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We show a close relationship between non-degenerate smooth commuting squares of II1-factors with horizontal inclusions of finite index and inclusions of subfactor planar algebras by showing that each leads to a construction of the other. One direction of this uses the Guionnet--Jones--Shlyakhtenko construction.
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The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.
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