6 papers
On semisimple quasitriangular Hopf algebras of dimension
Jingcheng Dong, Li Dai
Let be a prime number, be an odd square-free natural number, and be a non-negative integer. We prove that a semisimple quasitriangular Hopf algebra of dimension $dq^n…
Non-trivially graded self-dual fusion categories of rank
Jingcheng Dong, Liangyun Zhang, Li Dai
Let be a self-dual spherical fusion categories of rank with non-trivial grading. We complete the classification of Grothendieck ring of $\mathcal…
Integral almost square-free modular categories
Jingcheng Dong, Libin Li, Li Dai
We study integral almost square-free modular categories; i.e., integral modular categories of Frobenius-Perron dimension , where is a prime number, is a square-free n…
On Kaplansky's sixth conjecture
Li Dai, Jingcheng Dong
About years ago, Kaplansky conjectured that the dimension of a semisimple Hopf algebra over an algebraically closed field of characteristic zero is divisible by the dimensions…
Existence of Tannakian subcategories and its applications
Jingcheng Dong, Li Dai
We study several classes of braided fusion categories, and prove that they all contain nontrivial Tannakian subcategories. As applications, we classify some fusion categories in te…
On integral fusion categories with low-dimensional simple objects
Jingcheng Dong, Li Dai
Let be an algebraically closedfield of characteristic zero. In this paper we consider an integral fusion category over in which the Frobenius-Perron dimensions of its simpl…