We obtain a necessary condition for a strictly weakly integral generalized Tambara-Yamagami fusion category to be braided.Then we use this result to classify braided extensions of a pointed fusion category with prime dimension.
通过分析半单Hopf代数类群元所构成群的阶数,得到了特征为零代数闭域上pq3维半单Hopf代数的结构:它们或者是半可解的,或者同构于Radford双积R#A,其中:p,q是满足条件p>q2的素数;A是q3维半单Hopf代数;R是Yetter-Drinfeld模范畴A A Y D中的p维半单Hopf代数.
Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K（C） of C; that is, we prove that K（C） = Fib Z[Z2], where Fib is the Fibonacci fusion ring and Z[Z2] is the group ring on Z2. In particular, if C is braided, then it is equivalent to Fib Vecwz2 as fusion categories, where Fib is a Fibonacci category and Vecwz2 is a rank 2 pointed fusion category.
