Faithful simple objects, orders and gradings of fusion categories

SONIA NATALE

ALGEBRAIC AND GEOMETRIC TOPOLOGY

GEOMETRY & TOPOLOGY PUBLICATIONS

Lugar: Coventry, UK (University of Warwick); Año: 2013 vol. 13 p. 1489 - 1511

1472-2739

We establish some relations between the orders of simple objects in a fusion category and the structure of its universal grading group. We consider fusion categories which have a faithful simple object and show that its universal grading group must be cyclic. As for the converse, we prove that a braided nilpotent fusion category with cyclic universal grading group always has a faithful simple object. We study the universal grading of fusion categories with generalized TambaraYamagami fusion rules. As an application, we classify modular categories in this class and describe the modularizations of braided TambaraYamagami fusion categories.