Non-Abelian fractional supersymmetry in two dimensions

Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing U-q (sl(2,R)) at roots of unity. Its representations and the matrix elements are obtained. The dual of it is constructed and the corepresentations are studied. Moreover, a differential realization of the non-Abelian fractional supersymmetry generators is given in the generalized superspace defined by two commuting and two generalized Grassmann variables. An invariant action under the fractional supersymmetry transformations is given.