# MathSciDoc: An Archive for Mathematician ∫

#### Category TheoryRings and Algebrasmathscidoc:1701.04001

Acta Mathematica, 209, (1), 29-82, 2010.1
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 ( $${4},{3} + \sqrt {{3}}$$ ), 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 ofarXiv:0909.4099 [math.OA].
planar algebras; subfactors; skein theory; principal graphs
@inproceedings{stephen2010constructing,
title={Constructing the extended Haagerup planar algebra},
author={Stephen Bigelow, Emily Peters, Scott Morrison, and Noah Snyder},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203358749309757},
booktitle={Acta Mathematica},
volume={209},
number={1},
pages={29-82},
year={2010},
}

Stephen Bigelow, Emily Peters, Scott Morrison, and Noah Snyder. Constructing the extended Haagerup planar algebra. 2010. Vol. 209. In Acta Mathematica. pp.29-82. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203358749309757.