2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152214The purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well-known algebraic structures such as Gerstenhaber algebras and BV-algebras. Some applications are discussed. In particular, we found an explicit connection between the Koszul-Brylinski operator of a Poisson manifold and its modular class. As a consequence, we prove that Poisson homology is isomorphic to Poisson cohomology for unimodular Poisson structures.18 pages, LaTeXDifferential GeometryAlgebraic GeometryQuantum Algebratext