Drinfeld center of planar algebra

2012/03/18 by Das, Paramita, Ghosh, Shamindra Kumar, Gupta, Ved Prakash · 1 citation
#46L37 #Category Theory (math.CT) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1203.3958

Abstract

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra P (not necessarily having finite depth). We prove that if N ⊂ M is a subfactor realization of P, then the Drinfeld center of the N-N-bimodule category generated by _N L² (M)_M, is equivalent to the category of Hilbert affine representations of P satisfying certain finiteness criterion. As a consequence, we prove Kevin Walker's conjecture for planar algebras.

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