Quantum Deformation of the Poincare Supergroup and $��$-deformed Superspace

The classical $r$-matrix for $N=1$ superPoincar{��} algebra, given by Lukierski, Nowicki and Sobczyk is used to describe the graded Poisson structure on the $N=1$ Poincar{��} supergroup. The standard correspondence principle between the even (odd) Poisson brackets and (anti)commutators leads to the consistent quantum deformation of the superPoincar{��} group with the deformation parameter $q$ described by fundamental mass parameter $��\quad (��^{-1}=\ln{q})$. The $��$-deformation of $N=1$ superspace as dual to the $��$-deformed supersymmetry algebra is discussed.
Wroclaw University preprint IFTUWr 868 /94, March 1994, 12 pages