## Planar algebras and the Ocneanu-Szymanski theorem

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- by Paramita Das and Vijay Kodiyalam PDF
- Proc. Amer. Math. Soc.
**133**(2005), 2751-2759 Request permission

## Abstract:

We give a very simple ‘planar algebra’ proof of the part of the Ocneanu-Szymański theorem which asserts that for a finite index, depth two, irreducible $II_1$-subfactor $N \subset M$, the relative commutants $N^\prime \cap M_1$ and $M^\prime \cap M_2$ admit mutually dual Kac algebra structures. In the hyperfinite case, the same techniques also prove the other part, which asserts that $N^\prime \cap M_1$ acts on $M$ with invariants $N$.## References

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## Additional Information

**Paramita Das**- Affiliation: The Institute of Mathematical Sciences, Taramani, Chennai, India 600113
- Address at time of publication: Department of Mathematics and Statistics, University of New Hampshire, Durham, New Hampshire 03824
- Email: pdas@imsc.res.in, pnt2@unh.edu
**Vijay Kodiyalam**- Affiliation: The Institute of Mathematical Sciences, Taramani, Chennai, India 600113
- MR Author ID: 321352
- Email: vijay@imsc.res.in
- Received by editor(s): December 2, 2002
- Received by editor(s) in revised form: June 25, 2003
- Published electronically: April 19, 2005
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**133**(2005), 2751-2759 - MSC (1991): Primary 54C40, 14E20; Secondary 46E25, 20C20
- DOI: https://doi.org/10.1090/S0002-9939-05-07789-0
- MathSciNet review: 2146224