2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153661This paper extends Kontsevich's ideas on quantizing Poisson manifolds. A new differential is added to the Hodge decomposition of the Hochschild complex, so that it becomes a bicomplex, even more similar to the classical Hodge theory for complex manifolds.7 pages, LaTeX file, submitted to the proceedings of the 1996 Joint Summer Research Conference on QuantizationQuantum Algebra16S80, 16E40 (Primary) 81S10, 55P62 (Secondary)text