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Description

Izumi classified the non-commutative near-group fusion categories, that is, fusion categories with one non-invertible simple object and a non-abelian group of invertible objects. He showed, in particular, that the groups of invertible simple objects must be extra-special two groups. I will discuss joint work with Izumi toward computing the Frobenius-Schur indicators for these categories. We also establish some realizations of these categories as representation categories for bi-crossed product quasi-Hopf algebras.