In this work, we have studied the invariants of motion of two SU (N ) supersymmetric t-J models of 1/r 2 hopping and exchange in one dimension. The first model is defined on a lattice of equal spaced sites, and the second on a non-equal spacing lattice. Using the "exchange operator formalism", we are able to construct all the invariants for the models, by mapping the systems to mixtures of fermions and bosons. This identification shows that the supersymmetric t-J model on the chain with equal-spaced sites also belongs to Shastry-Sutherland's "Super-Lax-Pair" family.
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