A graphical approach to the Drinfeld centre

2019/11/17 by Hardiman, Leonard
#18D10 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1911.07271

Abstract

Let C be a spherical fusion category. The goal of this article is to present the tube category of C, denoted TC, as giving an alternative graphical perspective on the Drinfeld centre of C, denoted Z(C). We then exploit this perspective to obtain an alternative proof of the equivalence between Z(C) and C \boxtimes C when C is modular. Sections 2-4 provide a survey of the required prerequisites; readers already familiar with graphical calculus in fusion categories should start at Section 5.

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