{"title":"平面代数","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":"{\"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}","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}
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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