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Singly generated planar algebras of small dimension, Part II
Authors:Dietmar Bisch  Vaughan Jones
Affiliation:a Department of Mathematics, UC Santa Barbara, Santa Barbara, CA 93106, USA
b Department of Mathematics, UC Berkeley, Berkeley, CA 94720, USA
Abstract:We classified in Bisch and Jones (Duke Math. J. 101 (2000) 41) all spherical C∗-planar algebras generated by a non-trivial 2-box subject to the condition that the dimension of N′∩M2 is ?12. We showed that they are given by the Fuss-Catalan systems discovered in Bisch and Jones (Invent. Math. 128 (1997) 89) and one exceptional planar algebra. In the present paper, we extend these results and show that there is only one spherical C∗-planar algebra generated by a single non-trivial 2-box if the dimension of N′∩M2 is 13. It is given by the standard invariant of the crossed product subfactor View the MathML source, where D5 denotes the dihedral group with 10 elements.
Keywords:46L10   46L37
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