Fractional Spin through quantum affine Algebras with vanishing central charges

Abstract: Using the splitting of a Q-deformed boson, in the Q → q = e 2πik limit, the fractional decomposition of the quantum affine algebra Â(n) and the quantum affine super-algebra Â(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 Â(n) and the classical one in the fermionic realization