The legacy of Vaughan Jones in 𝐼𝐼₁ factors

Author:

Popa Sorin

Abstract

We describe Vaughan Jones’s ground-breaking discovery that symmetries ofII1\mathrm {II}_1factors, 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 ofII1\mathrm {II}_1factors.

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference69 articles.

1. The classification of subfactors with index at most 5\frac14;Afzaly, Narjess;Mem. Amer. Math. Soc.,2023

2. C. Anantharaman and S. Popa, An introduction to 𝐼𝐼₁ factors, \url{https://www.math.ucla.edu/ popa/Books/IIunV15.pdf}, 2021.

3. Constructing the extended Haagerup planar algebra;Bigelow, Stephen;Acta Math.,2012

4. Memories of Vaughan Jones;Bisch, Dietmar;Notices Amer. Math. Soc.,2021

5. Algebras associated to intermediate subfactors;Bisch, Dietmar;Invent. Math.,1997

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