2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50350Using the splitting of a $Q$-deformed boson, in the $Q \to q= e^{\frac{\rm 2πi}{\rm k}}$ limit, the fractional decomposition of the quantum affine algebra $\hat A(n)$ and the quantum affine superalgebra $\hat A(n,m)$ are found. This decomposition is based on the oscillator representation and can be related to the fractional supersymmetry and k-fermionic spin. We establish also the equivalence between the quantum affine algebra $\hat A(n)$ and the classical one in the fermionic realization.(17 pages, latex, non figures)High Energy Physics - Theorytext