JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.15, no.9, 2016 (SCI-Expanded)
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.