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|Paper IPM / Physic / 6831||
Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the N=1 super E2 algebra associated to the deformation of translations in a noncommutative Euclidean plane. The algebra is obtained using appropriate representaions of its generators on the space of superfields in a D=2, N=1 "noncommutative superspace." We find that the (anti)commutators between several (super)translation generators are 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.
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