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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $N$.
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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