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We produce an explicit embedding of the planar algebra of the Drinfeld double of a finite-dimensional, semisimple and cosemisimple Hopf algebra into the two-cabling of the planar algebra of the dual Hopf algebra .
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Sandipan De, Vijay Kodiyalam, Planar algebras, cabling and the Drinfeld double. Quantum Topol. 9 (2018), no. 1, pp. 141–165DOI 10.4171/QT/105