An analogue of Connes-Haagerup approach for classification of subfactors of the type III. (English) Zbl 1094.46034

Masuda, Toshihiko

J. Math. Soc. Japan 57, No. 4, 959-1001 (2005).

The paper is devoted to the classification of subfactors initiated by V. F. R. Jones [Invent. Math. 72, 1–25 (1983; Zbl 0508.46040)]. A significant contribution to this problem was made by S. Popa who proved that strongly amenable subfactors of type \(\mathrm{III}_1\) with the same type \(\mathrm{II}\) and type \(\mathrm{III}\) principal graphs are completely classified by their standard invariants. In the present paper, the author presents a different proof of this classification theorem, based on Connes’ and Haagerup’s arguments on the uniqueness of the injective factor of type \(\mathrm{III}_1\).

Reviewer: Sh. A. Ayupov (Tashkent)

MSC:

46L37	Subfactors and their classification
46L40	Automorphisms of selfadjoint operator algebras

Keywords:

subfactor of type \(\mathrm{III}_1\); standard invariants; symmetric enveloping algebras; relative bicentralizer; modular automorphisms

Citations:

Zbl 0508.46040