2-supertransitive subfactors at index $3+\sqrt{5}$

Abstract

This article proves the existence and uniqueness of a subfactor planar algebra with principal graph consisting of a diamond with arms of length 2 at opposite sides, which we call 2D2. We also prove the uniqueness of the subfactor planar algebra with principal graph 4442. We conjecture this will complete the list of subfactor planar algebras at index $3+\sqrt{5}$.

22 pages

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Cited by in corpus (5)

• Calculating two-strand jellyfish relations
• The classification of $3^n$ subfactors and related fusion categories
• Drinfeld centers of fusion categories arising from generalized Haagerup subfactors
• Classification of $\mathbb{Z}/2\mathbb{Z}$-quadratic unitary fusion categories
• A complete classification of unitary fusion categories tensor generated by an object of dimension $\frac{1+\sqrt{5}}{2}$