Z3-graded Cartan calculus on O( C1|1|1 q )

Abstract

After a brief introduction of the basic concepts of Z3-grading, the paper continues by introducing Z3-graded differential calculus and Z3-graded Cartan calculus. Then, using a matrix R which is a solution of the Yang-Baxter equation, a new Z3-graded quantum group and a Z3-graded quantum space are introduced. The scheme of the Z3-graded differential calculus developed on the algebra of functions on this quantum space is extended to the Z3-graded Cartan calculus and all the results obtained are formulated using the matrix R.