Supersymmetric Lorentz invariant deformations of superspaces

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor lambda(a) and Ramond Grassmannian vector psi(m) = -(1)/(2)(theta gamma(m)lambda) in the spinor realization(42) are proposed. The map of supergravity background into composite supercoordinates: (B-mn(-1), Psi(a)(m), C-ab)->(i psi(m)psi(n), psi(m)lambda(a), lambda(a)lambda(b)) valid up to the second order corrections in deformation parameter h and transforming the background dependent Lorentz noninvariant (anti) commutators of supercoordinates into their invaxiant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector psi(1m) = (1)/(2)(theta gamma(m)gamma(5)lambda) and to vanish for the theta components with the same chiralities. The deformations in the (super)twistor picture are discussed.