Factors of type II$_1$ without non-trivial finite index subfactors
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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.References
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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
- Received by editor(s): March 8, 2007
- Received by editor(s) in revised form: June 25, 2007
- Published electronically: November 17, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2471930