Factors of type II_1 without non-trivial finite index subfactors

Details Factors of type II_1 without non-trivial finite index subfactors Factors of type II_1 without non-trivial finite index subfactors

2006-10-06

arxiv.org/abs/math/0610231v2

Transactions of the American Mathematical Society 361 (2009), 2587-2606.

Mathematics

Operator Algebras

Smoothened presentation, final version

Scientific paper

We call a subfactor trivial if it is isomorphic with the obvious inclusion of N into matrices over N. We prove the existence of type II_1 factors M without non-trivial finite index subfactors. Equivalently, every M-M-bimodule with finite coupling constant, both as a left and as a right M-module, is a multiple of L^2(M). Our results rely on the recent work of Ioana, Peterson and Popa, who proved the existence of type II_1 factors without outer automorphisms.

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