Right-Covariant Differential Calculus on Hopf Superalgebra F(Cq2|1)

Abstract

We define a new Z(2)-graded quantum (2+1)-space and show that the extended Z(2)-graded algebra of polynomials on this Z(2)-graded quantum space, denoted by F(C-q(2|1)), is a Z(2)-graded Hopf algebra. We construct a right-covariant differential calculus on F(C-q(2|1)) and define a Z(2)-graded quantum Weyl algebra and mention a few algebraic properties of this algebra. Finally, we explicitly construct the dual Z(2)-graded Hopf algebra of F(C-q(2|1)).