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