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We propose an algebraic lattice supersymmetry formulation which has an exactsupersymmetry on the lattice. We show how lattice version of chiral conditionscan be imposed to satisfy an exact lattice supersymmetry algebra. The speciesdoublers of chiral fermions and the corresponding bosonic counterparts can beaccommodated to fit into chiral supermultiplets of lattice supersymmetry andthus lattice chiral fermion problem does not appear. We explicitly show how N=2Wess-Zumino model in one and two dimensions can be formulated to keep exactsupersymmetry for all super charges on the lattice. The momentum representationof N=2 lattice chiral sypersymmetry algebra has lattice periodicity and thusmomentum conservation should be modified to a lattice version of sine momentumconservation, which generates nonlocal interactions and leads to a loss oflattice translational invariance. It is shown that the nonlocality is mild andthe translational invariance is recovered in the continuum limit. In thecoordinate representation a new type of product is defined and the differenceoperator satisfies Leibnitz rule and an exact lattice supersymmetry is realizedon this product.

Species Doublers as Super Multiplets in Lattice Supersymmetry: Chiral Conditions of Wess-Zumino Model for D=N=2