On the minimal extension and structure of weakly group-theoretical braided fusion categories

2021/05/05 by Ostrik, Victor, Yu, Zhiqiang
#18M05 #18M20 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2105.01814

Abstract

We show that any slightly degenerate weakly group-theoretical fusion category admits a minimal non-degenerate extension. Let d be a positive square-free integer, given a weakly group-theoretical non-degenerate fusion category C, assume that FPdim(C)=nd and (n,d)=1. If (FPdim(X)²,d)=1 for all simple objects X of C, then we show that C contains a non-degenerate fusion subcategory C(ℤ_d,q). In particular, we obtain that integral fusion categories of FP-dimensions p^md such that C'⊆ sVec are nilpotent and group-theoretical, where p is a prime and (p,d)=1.

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