{"title":"沃恩琼斯的遗产在𝐼𝐼1因素","authors":"S. Popa","doi":"10.1090/bull/1805","DOIUrl":null,"url":null,"abstract":"<p>We describe Vaughan Jones’s ground-breaking discovery that symmetries of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper I normal upper I Subscript 1\">\n <mml:semantics>\n <mml:msub>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"normal\">I</mml:mi>\n <mml:mi mathvariant=\"normal\">I</mml:mi>\n </mml:mrow>\n <mml:mn>1</mml:mn>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\mathrm {II}_1</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> factors, as encoded by their subfactors, are quantized and have a natural index that can be non-integral. We then comment on the impact his revolutionary work had in the study of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper I normal upper I Subscript 1\">\n <mml:semantics>\n <mml:msub>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"normal\">I</mml:mi>\n <mml:mi mathvariant=\"normal\">I</mml:mi>\n </mml:mrow>\n <mml:mn>1</mml:mn>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\mathrm {II}_1</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> factors.</p>","PeriodicalId":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The legacy of Vaughan Jones in 𝐼𝐼₁ factors\",\"authors\":\"S. Popa\",\"doi\":\"10.1090/bull/1805\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We describe Vaughan Jones’s ground-breaking discovery that symmetries of <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"normal upper I normal upper I Subscript 1\\\">\\n <mml:semantics>\\n <mml:msub>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi mathvariant=\\\"normal\\\">I</mml:mi>\\n <mml:mi mathvariant=\\\"normal\\\">I</mml:mi>\\n </mml:mrow>\\n <mml:mn>1</mml:mn>\\n </mml:msub>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathrm {II}_1</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> factors, as encoded by their subfactors, are quantized and have a natural index that can be non-integral. We then comment on the impact his revolutionary work had in the study of <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"normal upper I normal upper I Subscript 1\\\">\\n <mml:semantics>\\n <mml:msub>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mi mathvariant=\\\"normal\\\">I</mml:mi>\\n <mml:mi mathvariant=\\\"normal\\\">I</mml:mi>\\n </mml:mrow>\\n <mml:mn>1</mml:mn>\\n </mml:msub>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\mathrm {II}_1</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> factors.</p>\",\"PeriodicalId\":9513,\"journal\":{\"name\":\"Bulletin of the American Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2023-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the American Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/bull/1805\",\"RegionNum\":3,\"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":"Bulletin of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/bull/1805","RegionNum":3,"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
摘要
我们描述了Vaughan Jones的突破性发现，即I I 1\mathrm的对称性{II}_1因子，由它们的子因子编码，是量化的，并且具有可以是非积分的自然索引。然后，我们评论了他的革命工作对I I 1\mathrm研究的影响{II}_1因素。
We describe Vaughan Jones’s ground-breaking discovery that symmetries of II1\mathrm {II}_1 factors, as encoded by their subfactors, are quantized and have a natural index that can be non-integral. We then comment on the impact his revolutionary work had in the study of II1\mathrm {II}_1 factors.
期刊介绍：
The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
