2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62448Let $D(H)$ be the quantum double associated to a finite dimensional quasi-Hopf algebra $H$. In this note, we first generalize a result of Majid, stating that a finite dimensional Hopf algebra $H$ is quasitriangular if and only if there is a projection of the quantum double $D(H)$ onto $H$ covering the natural inclusion.We then prove that the quantum double of a finite dimensional quasitriangular quasi-Hopf algebra is a biproduct.15 pagesQuantum AlgebraRings and Algebras16W30text