Differential Operators Over Quantum Spaces

The topic of this paper is the development of a differential calculus on a quantum space covariant with respect to the action of a quantum group. Quantized differential operators, jets, the de Rham and Spencer complexes, etc., are constructed. Also the integration over a quantum space, adjoint operators, integral forms, Greens formula are discussed. The Wess–Zumino de Rham complex and the algebra of differential operators are treated as a basic example.