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On braided near-group categories

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arxiv 1102.4640 v1 pith:OX5KZU22 submitted 2011-02-22 math.QA

Josiah Thornton This is my paper · ORCID
classification math.QA
keywords categoriesbraidedbraidingcategoryclassifycomeequippedexactly
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abstract

We prove that any fusion category over $\mathbb{C}$ with exactly one non-invertible simple object is spherical. Furthermore, we classify all such categories that come equipped with a braiding.

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  1. Anyons and Inherently Complex F-symbols

    cond-mat.str-el 2026-07 accept novelty 7.0 of 10

    Rep(Z7 ⋊ Z3) and Rep(Z5 ⋊ Z4) are the lowest-rank braided fusion categories known whose F-symbols are inherently complex, as proven by explicit non-real gauge-invariant quantities.

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