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.