A Two-parameter bicovariant differential calculus on the (1+2)-dimensional q-superspace

Abstract

We construct a two-parameter bicovariant differential calculus on R-q(1/2) with the help of the covariance point of view using the Hopf algebra structure of R-q(1/2). To achieve this, we first use the consistency of calculus and the approach of R-matrix which satisfies both ungraded and graded Yang-Baxter equations. In particular, based on this differential calculus, we investigate Cartan-Maurer forms for this q-superspace. Finally, we obtain the quantum Lie superalgebra corresponding the Cartan-Maurer forms.