2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231317We prove that the quantum double of the quasi-Hopf algebra A_q(g) of dimension n^{dim g} attached in arXiv:math/0403096 to a simple complex Lie algebra g and a primitive root of unity q of order n^2 is equivalent to Lusztig's small quantum group u_q(g) (under some conditions on n). We also give a conceptual construction of A_q(g) using the notion of de-equivariantization of tensor categories.latex, 6 pages; proof of Theorem 4.1 added, a few references addedQuantum Algebratext