We suggest a reduction of the globalization and multidimensional quantization to the case of reductive Lie groups by lifting to U(1)-covering. Our construction is connected with the M. Duflo's third method for algebraic groups. From a reductive datum of the givan real algebraic Lie group we firstly construct geometric complexes with respect to U(1)-covering by using the unipotent positive distributions. Then we discribe in terms of local cohomology the maximal globalization of Harish-Chandra modules which correspond to the geometric complexes.