Faithful simple objects, orders and gradings of fusion categories

Natale, Sonia

doi:10.2140/agt.2013.13.1489

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Faithful simple objects, orders and gradings of fusion categories

Sonia Natale

Algebraic & Geometric Topology 13 (2013) 1489–1511

DOI: 10.2140/agt.2013.13.1489

Abstract

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.

Keywords

fusion category, graded fusion category, faithful object, universal grading group

Mathematical Subject Classification 2010

Primary: 18D10, 16T05

References

Publication

Received: 7 October 2011

Revised: 29 October 2012

Accepted: 22 December 2012

Published: 30 April 2013

Authors

Sonia Natale
Facultad de Matemática, Astronomía y Física Universidad Nacional de Córdoba CIEM-CONICET Medina Allende s/n Ciudad Universitaria 5000 Córdoba Argentina
http://www.famaf.unc.edu.ar/~natale/

Volume 13, issue 3 (2013)