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2012 Constructing the extended Haagerup planar algebra
Stephen Bigelow, Emily Peters, Scott Morrison, Noah Snyder
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Acta Math. 209(1): 29-82 (2012). DOI: 10.1007/s11511-012-0081-7


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 of arXiv:0909.4099 [math.OA].


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Stephen Bigelow. Emily Peters. Scott Morrison. Noah Snyder. "Constructing the extended Haagerup planar algebra." Acta Math. 209 (1) 29 - 82, 2012.


Received: 31 January 2010; Published: 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1270.46058
MathSciNet: MR2979509
Digital Object Identifier: 10.1007/s11511-012-0081-7

Primary: 46L37
Secondary: 18D10

Keywords: planar algebras , principal graphs , skein theory , subfactors

Rights: 2012 © Institut Mittag-Leffler

Vol.209 • No. 1 • 2012
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