Nontrivial Extensions of the 3D-Poincaré Algebra and Fractional Supersymmetry for Anyons

@article{Traubenberg1996NontrivialEO,
  title={Nontrivial Extensions of the 3D-Poincar{\'e} Algebra and Fractional Supersymmetry for Anyons},
  author={Michel Rausch de Traubenberg and Marcus J. Slupinski},
  journal={Modern Physics Letters A},
  year={1996},
  volume={12},
  pages={3051-3066}
}
Nontrivial extensions of three-dimensional Poincare algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three-dimensional generalizations of fractional supersymmetry of order F already considered in one and two dimensions. Representations of these algebras are exhibited, and unitarity is explicitly checked. It is then shown that these extensions generate symmetries which connect fractional spin states or anyons. Finally, a natural… 

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