Two-dimensional fractional supersymmetry from the quantum Poincaré group at roots of unity

A group theoretical understanding of the two-dimensional fractional supersymmetry is given in terms of the quantum Poincaré group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the pseudo-unitary and irreducible representations of them are obtained. The matrix elements of these representations are explicitly constructed.