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Factors of type II$ _1$ without non-trivial finite index subfactors


Author: Stefaan Vaes
Journal: Trans. Amer. Math. Soc. 361 (2009), 2587-2606
MSC (2000): Primary 46L37; Secondary 46L54
DOI: https://doi.org/10.1090/S0002-9947-08-04585-6
Published electronically: November 17, 2008
MathSciNet review: 2471930
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Abstract: We call a subfactor $ N \subset M$ trivial if it is isomorphic with the obvious inclusion of $ N$ in $ \operatorname{M}_n(\mathbb{C}) \otimes 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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Additional Information

Stefaan Vaes
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B–3001 Leuven, Belgium
Email: stefaan.vaes@wis.kuleuven.be

DOI: https://doi.org/10.1090/S0002-9947-08-04585-6
Received by editor(s): March 8, 2007
Received by editor(s) in revised form: June 25, 2007
Published electronically: November 17, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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