2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184556Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra isomorphic to the Ocneanu double triangle algebra.28 pages, 4 figures, new typesetting and a few correctionsHigh Energy Physics - TheoryMathematical PhysicsQuantum AlgebraQuantum symmetries of faces models and the double triangle algebratext