Author: Alexander Verbovetsky

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, Green's formula are discussed. The Wess-Zumino de Rham complex and the algebra of differential operators are treated as a basic example.

To appear in Acta Applicandae Math.

28 pages. AmS-TeX. To compile source files (.tex) one needs the title page style files titams.tex.