ﻻ يوجد ملخص باللغة العربية
We show any slightly degenerate weakly group-theoretical fusion category admits a minimal extension. Let $d$ be a positive square-free integer, given a weakly group-theoretical non-degenerate fusion category $mathcal{C}$, assume that $text{FPdim}(mathcal{C})=nd$ and $(n,d)=1$. If $(text{FPdim}(X)^2,d)=1$ for all simple objects $X$ of $mathcal{C}$, then we show that $mathcal{C}$ contains a non-degenerate fusion subcategory $mathcal{C}(mathbb{Z}_d,q)$. In particular, we obtain that integral fusion categories of FP-dimensions $p^md$ such that $mathcal{C}subseteq text{sVec}$ are nilpotent and group-theoretical, where $p$ is a prime and $(p,d)=1$.
For a braided fusion category $mathcal{V}$, a $mathcal{V}$-fusion category is a fusion category $mathcal{C}$ equipped with a braided monoidal functor $mathcal{F}:mathcal{V} to Z(mathcal{C})$. Given a fixed $mathcal{V}$-fusion category $(mathcal{C}, m
We show that the core of a weakly group-theoretical braided fusion category $C$ is equivalent as a braided fusion category to a tensor product $B boxtimes D$, where $D$ is a pointed weakly anisotropic braided fusion category, and $B cong vect$ or $B$
We prove that representations of the braid groups coming from weakly group-theoretical braided fusion categories have finite images.
This is a study of weakly integral braided fusion categories with elementary fusion rules to determine which possess nondegenerately braided extensions of theoretically minimal dimension, or equivalently in this case, which satisfy the minimal modula
We first show that every group-theoretical category is graded by a certain double coset ring. As a consequence, we obtain a necessary and sufficient condition for a group-theoretical category to be nilpotent. We then give an explicit description of t