Constructing the extended Haagerup planar algebra
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11511_2012_Article_81.pdf
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Author(s)
Bigelow, Stephen
Peters, Emily
Morrison, Scott
Snyder, Noah
Date Issued
September 2012
Journal
Acta Mathematica
Publisher
Springer Netherlands
Citation
Bigelow, Stephen et al. “Constructing the Extended Haagerup Planar Algebra.” Acta Mathematica 209.1 (2012): 29–82.
Version
Author's final manuscript
Abstract
We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the ‘extended Haagerup’ principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range (4,3+√3), which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein-theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein-theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram. This is the published version of arXiv:0909.4099 [math.OA].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s11511-012-0081-7
