Popa 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 this paper, we present a different proof of this classification theorem based on Connes and Haagerup's arguments on the uniqueness of the injective factor of type $\mathrm{III}_1$ .
Publié le : 2005-10-14
Classification:
subfactors of type $\mathrm{III}_1$,
standard invariants,
symmetric enveloping algebras,
relative bicentralizer,
modular automorphisms,
46L37,
46L40
@article{1150287301,
author = {MASUDA, Toshihiko},
title = {An analogue of Connes-Haagerup approach for classification of subfactors of type III$\_{\bf 1}$},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 959-1001},
language = {en},
url = {http://dml.mathdoc.fr/item/1150287301}
}
MASUDA, Toshihiko. An analogue of Connes-Haagerup approach for classification of subfactors of type III$_{\bf 1}$. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 959-1001. http://gdmltest.u-ga.fr/item/1150287301/