An over-parametrized (three-parametric) R-matrix satisfying a graded Yang-Baxter equation is introduced. It turns out that such an over-parametrization is very helpful. Indeed, this R-matrix with one of the parameters being auxiliary, thus, reducible to a two-parametric R-matrix, allows the construction of quantum supergroups GLp,q(1/1) and Up,q[gl(1/1)] which, respectively, are two-parametric deformations of the supergroup GL(1/1) and the universal enveloping algebra U[gl(1/1)]. | Quasi three parametric r matrix and quantum supergroups GLp,q(1/1) and Up,q[gl(1/1)]
