The legacy of Vaughan Jones in 𝐼𝐼₁ factors

IF 2 3区数学 Q1 MATHEMATICS

Bulletin of the American Mathematical Society Pub Date : 2023-07-05 DOI:10.1090/bull/1805

S. Popa

{"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":" ","pages":""},"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}

引用次数: 0

Abstract

We describe Vaughan Jones’s ground-breaking discovery that symmetries of I I 1 \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 I I 1 \mathrm {II}_1 factors.

查看原文本刊更多论文

沃恩琼斯的遗产在𝐼𝐼1因素

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Bulletin of the American Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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.