Some properties of group-theoretical categories
Quantum Algebra
2010-01-08 v1 Category Theory
Abstract
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.
Cite
@article{arxiv.0709.4326,
title = {Some properties of group-theoretical categories},
author = {Shlomo Gelaki and Deepak Naidu},
journal= {arXiv preprint arXiv:0709.4326},
year = {2010}
}
Comments
Latex, 11 pages