A New Z₃-Graded Quantum Space And Its Geometry

In this article, we initially define an R-matrix with rank 9. Through the application of the "quantum group relation", we derive a Z(3)-graded quantum group, denoted by GL(q)(1|1|1), representing the group of 3x3 matrices. By introducing a Z(3)-graded quantum space, denoted by C-1|1|1 (q) , along with its exterior algebra, we formulate two Z(3)-graded differential calculi which are covariant with respect to the Z(3)-graded Hopf algebra of functions on the Z3-graded quantum group GL(q)(1|1|1).