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A complete classification of unitary fusion categories tensor generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$ (1904.08909v2)
Published 18 Apr 2019 in math.QA and math.CT
Abstract: In this paper we give a complete classification of unitary fusion categories $\otimes$-generated by an object of dimension $\frac{1 + \sqrt{5}}{2}$. We show that all such categories arise as certain wreath products of either the Fibonacci category, or of the dual even part of the $2D2$ subfactor. As a by-product of proving our main classification result we produce a classification of finite unitarizable quotients of $\operatorname{Fib}{*N}$ satisfying a certain symmetry condition.