# Fusion categories containing a fusion subcategory with maximal rank

@inproceedings{Dong2021FusionCC, title={Fusion categories containing a fusion subcategory with maximal rank}, author={Jingcheng Dong and Gang Chen and Zhihua Wang}, year={2021} }

In this paper, we study fusion categories which contain a proper fusion subcategory with maximal rank. They can be viewed as generalizations of near-group fusion categories. We first prove that they admit spherical structure. We then classify those which are nondegenerate or symmetric. Finally, we classify such fusion categories of rank 4.

#### References

SHOWING 1-10 OF 25 REFERENCES

PIVOTAL FUSION CATEGORIES OF RANK 3

- Mathematics
- 2014

We classify all fusion categories of rank 3 that admit a pivotal structure over an algebraically closed field of characteristic zero. Also in the Appendix (joint with D. Nikshych) we give some… Expand

Fusion categories of rank 2

- Mathematics
- 2002

We classify semisimple rigid monoidal categories with two isomorphism classes of simple objects over the field of complex numbers. In the appendix written by P.Etingof it is proved that the number of… Expand

Near-group categories

- Mathematics
- 2003

We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Con- ditions are given for the existence or nonexistence of coherent… Expand

Nilpotent fusion categories

- Mathematics
- 2006

Abstract In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion… Expand

On braided fusion categories I

- Mathematics
- 2009

We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups. We also give a comprehensive and… Expand

Frobenius property for fusion categories of small integral dimension

- Mathematics
- 2015

Let k be an algebraically closed field of characteristic zero. In this paper, we prove that fusion categories of Frobenius–Perron dimensions 84 and 90 are of Frobenius type. Combining this with… Expand

Tensor Categories with Fusion Rules of Self-Duality for Finite Abelian Groups

- Mathematics
- 1998

Abstract Semisimple tensor categories with fusion rules of self-duality for finite abelian groups are classified. As an application, we prove that the Tannaka duals of the dihedral and the quaternion… Expand

On fusion categories

- Mathematics
- 2002

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show… Expand

Module categories, weak Hopf algebras and modular invariants

- Mathematics
- 2001

AbstractWe develop a theory of module categories over monoidal categories (this is a
straightforward categorization of modules over rings). As applications we show that any
semisimple monoidal… Expand

On the classification of the Grothendieck rings of non-self-dual modular categories☆

- Mathematics
- 2010

Abstract We develop a symbolic computational approach to classifying low-rank modular fusion categories, up to finite ambiguity. By a generalized form of Ocneanu rigidity due to Etingof, Ostrik and… Expand