Acta Mathematica

, Volume 209, Issue 1, pp 29–82

Constructing the extended Haagerup planar algebra

  • Stephen Bigelow
  • Emily Peters
  • Scott Morrison
  • Noah Snyder

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 algebras subfactors skein theory principal graphs 

2000 Math. Subject Classification

primary 46L37 secondary 18D10 

Copyright information

© Institut Mittag-Leffler 2012

Authors and Affiliations

  • Stephen Bigelow
    • 1
  • Emily Peters
    • 2
  • Scott Morrison
    • 3
  • Noah Snyder
    • 4
  1. 1.Department of MathematicsUniversity of California, Santa BarbaraSanta BarbaraUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Mathematical Sciences InstituteAustralian National UniversityActonAustralia
  4. 4.Department of MathematicsIndiana University, BloomingtonBloomingtonUSA

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