The legacy of Vaughan Jones in 𝐼𝐼₁ factors

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials 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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/bull/1805","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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.