2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157992The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We propose a version of the algebraic index theorem for a Poisson manifold which is based on this trace density map.accepted to Journal fur die reine und angewandte MathematikQuantum AlgebraHigh Energy Physics - TheoryK-Theory and Homologytext