Noncommutative supersymmetry in two dimensions

Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the N = 1 super E-2 algebra associated to the deformation of translations in a noncommutative Euclidean plane. The algebra is obtained using appropriate representations of its generators on the space of superfields in a D = 2, N = 1 "noncommutative superspace." We find that the (anti) commutators of several (super)translation generators axe no longer vanishing, but involve a new set of generators which together with the (super)translation and rotation generators form a consistent closed algebra. We then analyze the spectrum of this algebra in order to obtain its fundamental and adjoint representations.