{"title":"Planar algebras","authors":"Vaughan Jones","doi":"10.53733/172","DOIUrl":null,"url":null,"abstract":"\n \n \nWe introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II1 factor, and vice versa. \n \n \n","PeriodicalId":30137,"journal":{"name":"New Zealand Journal of Mathematics","volume":"86 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"New Zealand Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.53733/172","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II1 factor, and vice versa.
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