Generalized supersymmetry and L\'evy-Leblond equation

The symmetries of the L\'evy-Leblond equation are investigated beyond the standard Lie framework. It is shown that the equation has two remarkable symmetries. One is given by the super Schr\"odinger algebra and the other one by a $\ZZ$ graded Lie algebra. The $\ZZ$ graded Lie algebra is achieved by transforming bosonic into fermionic operators in the super Schr\"odinger algebra and introducing second order differential operators as generators of symmetry.