2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54099A set of compatible formulas for the Clebsch-Gordan coefficients of the quantum algebra $U_{q}({\rm su}_2)$ is given in this paper. These formulas are $q$-deformations of known formulas, as for instance: Wigner, van der Waerden, and Racah formulas. They serve as starting points for deriving various realizations of the unit tensor of $U_{q}({\rm su}_2)$ in terms of $q$-boson operators. The passage from the one-parameter quantum algebra $U_{q }({\rm su}_2)$ to the two-parameter quantum algebra $U_{qp}({\rm u}_2)$ is discussed at the level of Clebsch-Gordan coefficients.15 pages, Tex FileHigh Energy Physics - Theorytext