2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221912We give generators and relations for the planar algebras corresponding to $ADE$ subfactors. We also give a basis and an algorithm to express an arbitrary diagram as a linear combination of these basis diagrams.Quantum AlgebraOperator Algebras46L37; 57M15; 46M99text