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

M. Mansour·M. Daoud
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Abstract

Using 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.

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M. Mansour, M. Daoud. 2000-10-29. Fractional Spin through Quantum Affine Algebra $\hat A(n)$ and quantum affine superalgebra $\hat A(n,m)$. https://arxiv.org/abs/hep-th/0010267

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