Fractional supersymmetry and Fth-roots of representations

@article{Traubenberg1999FractionalSA,
  title={Fractional supersymmetry and Fth-roots of representations},
  author={Michel Rausch de Traubenberg and Marcus J. Slupinski},
  journal={Journal of Mathematical Physics},
  year={1999},
  volume={41},
  pages={4556-4571}
}
A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of three-dimensional fractional supersymmetry in this framework needs some care. The proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation D of any Lie algebra g. This involves taking the Fth-roots of D in an appropriate sense. A fractional… 
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