DIFFERENTIAL CALCULUS ON THE LOGARITHMIC EXTENSION OF THE QUANTUM 3D SPACE AND WEYL ALGEBRA

Abstract

Noncommutative derivative operators acting on the quantum 3D space in the sense of Manin are introduced. Furthermore, the quantum 3D space is extended by the series expansion of the logarithm of the grouplike generator in the quantum 3D space. We give its differential calculus and the corresponding Weyl algebra. We also obtain algebra of Cartan–Maurer forms on this extension and the corresponding Lie algebra of vector fields. All noncommutative results are found to reduce to those of the standard commutative algebra when the deformation parameter of the quantum 3D space is set to one.