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 (not necessarily having finite depth). We prove that if is a subfactor realization of , then the Drinfeld center of the --bimodule category generated by , is equivalent to the category of Hilbert affine representations of 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