2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110216A Poisson geometry arising from maximal commutative subalgebras is studied. A spectral sequence convergent to Hochschild homology with coefficients in a bimodule is presented. It depends on the choice of a maximal commutative subalgebra inducing appropriate filtrations. Its E^{2}_{p,q}-groups are computed in terms of canonical homology with values in a Poisson module defined by a given bimodule and a maximal commutative subalgebra.10 pagesK-Theory and HomologyQuantum Algebra16E40; 81T30text