Some properties of group-theoretical categories

Details Some properties of group-theoretical categories Some properties of group-theoretical categories

2007-09-27

arxiv.org/abs/0709.4326v1

J. Algebra 322 (2009), no. 8, 2631-2641

Mathematics

Quantum Algebra

Latex, 11 pages

Scientific paper

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.

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