2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58324An explicit form of the generators of quantum and ordinary semisimple algebras for an arbitrary finite-dimensional representation is found. The generators corresponding to the simple roots are obtained in terms of a solution of a system of matrix equations. The result is presented in the form of $N_l\times N_l$ matrices, where $N_l$ is the dimension of the corresponding representation, determined by the invariant Weyl formula.LaTeX, 20 pagesMathematical Physicstext