Some properties of group-theoretical categories
Gelaki, Shlomo · Naidu, Deepak
Original · EN
We first show that every group-theoretical category is graded by a certain double coset ring. As a consequence, we obtain a necessary and sufficient condition for a group-theoretical category to be nilpotent. We then give an explicit description of the simple objects in a group-theoretical category (following Ostrik, arXiv:math/0202130) and of the group of invertible objects of a group-theoretical category, in group-theoretical terms. Finally, under certain restrictive conditions, we describe the universal grading group of a group-theoretical category.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.