On an analogue of a Brauer theorem for fusion categories

2015/03/16 by Sebastian Burciu, Burciu, Sebastian
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CT #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1503.04601

First draft, comments and suggestions are very welcome!

arxiv created 2015/03/16 · arxiv updated 2015/03/17

Abstract

In this paper we prove an analogue of Brauer's theorem for faithful objects in fusion categories. Other notions, such as the order and the index associated to faithful objects of fusion categories are also discussed. We show that the index of a faithful simple object of a fusion categories coincides with the order of the universal grading group of the fusion category.

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