REALIZATIONS OF THE POINCARE ALGEBRA AND POINCARE-INVARIANT EQUATIONS IN THREE-DIMENSIONAL SPACE-TIME

We have constructed all inequivalent, realizations of the Lie algebra Aof the Poincare group P(l,2) by Lie vector fields in three independent Aand one depen-dent variables. We have also obtained new second-order Adifferential equations inthree-dimensional space-time invariant under Athe group P(l,2).