Z3-GRADED DIFFERENTIAL CALCULUS ON THE QUANTUM SPACE Rq3

Abstract

In this work, the Z(3)-graded differential calculus of the extended quantum 3d space is constructed. By using this differential calculus, we obtain the algebra of Cartan-Maurer forms and the corresponding quantum Lie algebra. To give a Z(3)-graded Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on this space is extended by introducing inner derivations and Lie derivatives.