Acta Mathematica

, Volume 209, Issue 1, pp 29–82

Constructing the extended Haagerup planar algebra


  • Stephen Bigelow
    • Department of MathematicsUniversity of California, Santa Barbara
    • Department of MathematicsMassachusetts Institute of Technology
  • Scott Morrison
    • Mathematical Sciences InstituteAustralian National University
  • Noah Snyder
    • Department of MathematicsIndiana University, Bloomington

DOI: 10.1007/s11511-012-0081-7

Cite this article as:
Bigelow, S., Peters, E., Morrison, S. et al. Acta Math (2012) 209: 29. 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].


planar algebrassubfactorsskein theoryprincipal graphs

2000 Math. Subject Classification

primary 46L37secondary 18D10

Copyright information

© Institut Mittag-Leffler 2012