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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Planar algebras and the Ocneanu-Szymanski theorem


Authors: Paramita Das and Vijay Kodiyalam
Journal: Proc. Amer. Math. Soc. 133 (2005), 2751-2759
MSC (1991): Primary 54C40, 14E20; Secondary 46E25, 20C20
Published electronically: April 19, 2005
MathSciNet review: 2146224
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Abstract: We give a very simple `planar algebra' proof of the part of the Ocneanu-Szymanski 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 $N$.


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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
Email: vijay@imsc.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07789-0
PII: S 0002-9939(05)07789-0
Keywords: Planar algebra, subfactor, Kac algebra, Ocneanu-Szyma\'{n}ski theorem
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.