Fractional Spin through Quantum Affine Algebra $\widehat{A}(n)$ and quantum affine superalgebra $\widehat{A}(n,m)$

Using the splitting of a $Q$-deformed boson, in the $Q \to q= e^{\frac{\rm 2\pi i}{\rm k}}$ limit, the fractional decomposition of the quantum affine algebra $\widehat{A}(n)$ and the quantum affine superalgebra $\widehat{A}(n,m)$ 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 $\widehat{A}(n)$ and the classical one in the fermionic realization.