2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62895We develop a theory of quasi-Lie bialgebroids using a homological approach. This notion is a generalization of quasi-Lie bialgebras, as well as twisted Poisson structures with a 3-form background which have recently appeared in the context of string theory, and were studied by Ševera and Weinstein using a different method.The souped-up published version: section on gauge transformations and a few other remarks added. addedQuantum AlgebraMathematical PhysicsSymplectic Geometry53D05, 81T70; 51P05, 81T45text