SUPERSYMMETRIES OF THE SUPERSPACE E(3 2)

The superspace E(3\2) is the simplest superspace that generalizes the three-dimensional ordinary space. A super-Euclidean metric is defined on this superspace through its isomorphy with the vectorial representa tion superspace of the super-rotation algebra osp(1\2). The supergroup UOSP(3\2) is defined as the largest supersymmetry group acting in E(3 \2) and preserving the scalar product. The vectorial representation of the superrotation group, UOSP(1\2), acts also in E(3\2). The relation s between these two supersymmetries are studied exhaustively.