$Z_{3} -graded$ dıfferentıal calculus on the quantum space $R^{3}_{q}$

Abstract

In this work, the Z3 -graded differential calculus of the extended quan- tum 3d space is constructed. By using this differential calculus, we obtain the algebra of Cartan-Maurer forms and the corresponding quan- tum Lie algebra. To give a Z3 -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.