اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Jordan-H older theorem for weakly group-theoretical fusion categories
145
0
0.0
(
0
)
تأليف
Sonia Natale
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove a version of the Jordan-H older theorem in the context of weakly group-theoretical fusion categories. This allows us to introduce the composition factors and the length of such a fusion category C, which are in fact Morita invariants of C.
قيم البحث
اقرأ أيضاً
We prove that representations of the braid groups coming from weakly group-theoretical braided fusion categories have finite images.
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 $text{FPdim}(mat
hcal{C})=nd$ 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 $(p,d)=1$.
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 $B$
is an Ising braided category. In particular, if $C$ is integral, then its core is a pointed weakly anisotropic braided fusion category. As an application we give a characterization of the solvability of a weakly group-theoretical braided fusion category. We also prove that an integral modular category all of whose simple objects have Frobenius-Perron dimension at most 2 is necessarily group-theoretical.
We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category ${mathcal C}$ to be equivalent. This concludes the classification of such module categories.
The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of partitions
(more general; due to Maassen, 2018). We generalize these results to the case of graph categories, which allows to replace the symmetric group by the group of automorphisms of some graph.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
