2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/199031We study the relations between $q$-deformations and $q$-coherent states of the single oscillator representations for $su_q(1,1)$ and $su_q(2)$ algebras; Dyson and Holstein-Primakoff type in terms of Biedenharn, Macfarlane and anyonic oscilators. We also discuss the related Fock-Bargmann $q$-derivative and integration.19 pages, Revtex, no figuresQuantum AlgebraHigh Energy Physics - Theorytext