Non-Trivial Extensions of the 3D-Poincar\'e Algebra and Fractional   Supersymmetry for Anyons
  Non-trivial extensions of the three dimensional Poincar\'e 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 classification arises according to the decomposition of $F$ into its product of prime numbers leading to sub-systems with smaller symmetries. 
M. Rausch de Traubenberg, M. J. Slupinski