2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61768Let H be a differential graded Hopf algebra over a field k. This paper gives an explicit construction of a triple cochain complex that defines the Hochschild-Cartier cohomology of H. A certain truncation of this complex is the appropriate setting for deforming H as an H(q)-structure. The direct limit of all such truncations is the appropriate setting for deforming H as a strongly homotopy associative structure. Sign complications are systematically controlled. The connection between rational perturbation theory and the deformation theory of certain free commutative differential graded algebras is clarified.21 pages, 4 figuresAlgebraic TopologyCommutative AlgebraRings and Algebras16W30; 13D10; 16E45; 55P62text