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On finiteness of the set of intermediate subfactors


Authors: M. Khoshkam and B. Mashood
Journal: Proc. Amer. Math. Soc. 132 (2004), 2939-2944
MSC (2000): Primary 46L37
DOI: https://doi.org/10.1090/S0002-9939-04-07448-9
Published electronically: May 21, 2004
MathSciNet review: 2063113
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Abstract: For type $II_1$ factors $N\subset L$ with $[L:N]<\infty$, we show that the sets $\mathcal{L}_1=\{M\in \mathcal{L}(N\subset L)\colon N'\cap L \subset M\}$ and $\mathcal{L}_2=\{M\in \mathcal{L}(N\subset L)\colon N'\cap L =M'\cap L\}$ are finite. Moreover, $\mathcal{L}(N\subset L)$, the set of intermediate subfactors, is finite if and only if it is equal to $\mathcal{L}_1\cup \mathcal{L}_2$. If $N$ is an irreducible subfactor, then we recover a result of Y. Watatani.


References [Enhancements On Off] (What's this?)

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Additional Information

M. Khoshkam
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6

B. Mashood
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6

DOI: https://doi.org/10.1090/S0002-9939-04-07448-9
Keywords: Subfactors, von Neumann algebras, Jones index, lattice, relative commutants
Received by editor(s): May 30, 2001
Received by editor(s) in revised form: August 30, 2001, and October 23, 2002
Published electronically: May 21, 2004
Additional Notes: The first author’s research was supported by an NSERC grant
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society

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