The Structure of Sectors¶Associated with Longo–Rehren Inclusions¶I. General Theory

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From subfactors to categories and topology. II. The quantum double of tensor categories and subfactors (2001, methodology): “Following [19] we consider the element t ∈ ΞL defined by”
Cyclotomic Integers, Fusion Categories, and Subfactors (2010, background): “The dimension ( √ 3+ √ 7)/2 occurs in a fusion category constructed by Ostrik in the appendix based on an unpublished construction via a conformal inclusion (due to Xu [33]) of a subfactor originally constructed by Izumi [18].”
From subfactors to categories and topology. I. Frobenius algebras in and Morita equivalence of tensor categories (2001, background): “Those aspects of subfactor theory [40,23] which most directly inspired the present investigation and [47] were in fact done in the type III setting.”
Problems on invariants of knots and 3-manifolds (2004, methodology): “Then we can construct a new modular category C2 containing C1 as a full subcategory by the “quantum double” construction [315, 316, 182], but there may be another extension of C1 to a modular category.”