Bicovariant differential calculus on the quantum superspace R-q(1 vertical bar 2)

Super-Hopf algebra structure on the function algebra on the extended quantum super-space has been defined. It is given a bicovariant differential calculus on the superspace. The corresponding (quantum) Lie superalgebra of vector fields and its Hopf algebra structure are obtained. The dual Hopf algebra is explicitly constructed. A new quantum supergroup that is the symmetry group of the differential calculus is found.