English

Drinfeld center of planar algebra

Quantum Algebra 2026-01-01 v2 Category Theory Operator Algebras

Abstract

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra PP (not necessarily having finite depth). We prove that if NMN \subset M is a subfactor realization of PP, then the Drinfeld center of the NN-NN-bimodule category generated by NL2(M)M_N L^2 (M)_M, is equivalent to the category of Hilbert affine representations of PP satisfying certain finiteness criterion. As a consequence, we prove Kevin Walker's conjecture for planar algebras.

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Cite

@article{arxiv.1203.3958,
  title  = {Drinfeld center of planar algebra},
  author = {Paramita Das and Shamindra Kumar Ghosh and Ved Prakash Gupta},
  journal= {arXiv preprint arXiv:1203.3958},
  year   = {2026}
}

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32 pages