What question did this study set out to answer?

This research aims to explore the structure of quantum affine algebras at the roots of unity and their connections to fractional supersymmetry.

May 6, 2026Open Access

Quantum Affine Algebras at Roots of Unity and Fractional Spin

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Authors

MMMostafa Mansour

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Implication

Research demonstrates equivalence of quantum affine enveloping algebras at roots of unity in a k-fermionic framework, suggesting new insights into fractional supersymmetry.

Key Points

This research aims to explore the structure of quantum affine algebras at the roots of unity and their connections to fractional supersymmetry.
Investigated quantum affine enveloping algebras U_Q(\hat{A}(n)) and U_Q(\widehat{C}(n)) at Q = q = e^{2i\pi/k}
Utilized bosonic Fock representation to analyze the algebras' structure
Established equivalence with classical algebras under fermionic realization
Demonstrated that the deformation parameter collapses while preserving the representation-theoretic structure
Showed nilpotency conditions enforce module content truncation consistent with k-fermionic statistics

Cite This Study

Mostafa Mansour (2004) studied this question.

synapsesocial.com/papers/69fa97ce04f884e66b5319ab https://doi.org/10.5281/zenodo.20023906

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Implication

Research demonstrates equivalence of quantum affine enveloping algebras at roots of unity in a k-fermionic framework, suggesting new insights into fractional supersymmetry.

Quantum Affine Algebras at Roots of Unity and Fractional Spin

Discussion

Member takes

Implication

Key Points

Cite This Study

Quantum Affine Algebras at Roots of Unity and Fractional Spin

Discussion

Member takes

Implication

Key Points

Cite This Study

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