Geodesic
Faithful simple objects, orders and gradings of fusion categories
Natale, Sonia1
1Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM-CONICET, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina
Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1489-1511
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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 that have a faithful simple object and show that their universal grading groups 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 Tambara–Yamagami fusion rules. As an application, we classify modular categories in this class and describe the modularizations of braided Tambara–Yamagami fusion categories.

DOI : 10.2140/agt.2013.13.1489
Classification : 18D10, 16T05
Keywords: fusion category, graded fusion category, faithful object, universal grading group

Natale, Sonia  1

1 Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM-CONICET, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina 
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Natale, Sonia. Faithful simple objects, orders and gradings of fusion categories. Algebraic and Geometric Topology, Tome 13 (2013) no. 3, pp. 1489-1511. doi: 10.2140/agt.2013.13.1489

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