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arXiv · 0909.4099

Constructing the extended Haagerup planar algebra

Stephen Bigelow·Scott Morrison·Emily Peters·Noah Snyder
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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 $(4,3+\sqrt{3})$, 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.

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Stephen Bigelow, Scott Morrison, Emily Peters, Noah Snyder. 2009-09-22. Constructing the extended Haagerup planar algebra. https://doi.org/10.1007/s11511-012-0081-7

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