Constructing the extended Haagerup planar algebra

Stephen Bigelow Department of Mathematics, University of California, Santa Barbara Emily Peters Department of Mathematics, Massachusetts Institute of Technology Scott Morrison Mathematical Sciences Institute, Australian National University Noah Snyder Department of Mathematics, Indiana University, Bloomington

Category Theory Rings and Algebras mathscidoc: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
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  title={Constructing the extended Haagerup planar algebra},
  author={Stephen Bigelow, Emily Peters, Scott Morrison, and Noah Snyder},
  booktitle={Acta Mathematica},
Stephen Bigelow, Emily Peters, Scott Morrison, and Noah Snyder. Constructing the extended Haagerup planar algebra. 2010. Vol. 209. In Acta Mathematica. pp.29-82.
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