Some aspects of q- and qp- boson calculus

A set of compatible formulas for the Clebsch-Gordan coefficients of the quantum algebra Uq(su2) 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 Uq(su2) in terms of q-boson operators. the passage from the one-parameter quantum algebra Uq(su2) to the two-parameter quantum algebra Uqp(u2) is discussed at the level of Clebsch-Gordan coefficients. (authors)