On the two-parameter quantum supergroups and quantum superplanes

Abstract

Starting from the assumption that the generators of quantum supergroup are not supercommutatives with the coordinates of quantum superplane instead of usual supercommutativity in the Manin approach, we construct in a natural way the two-parameter quantum supergroup. The virtue of this formulation is that it leads to many probable quantum superplanes associated with a given quantum supergroup. Some interesting examples are presented. As a by-product of this formulation, a correspondence between the one- and two-parameter deformed differential structures on the quantum superplane is presented.