2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62887For a commutative algebra the shuffle product is a morphism of complexes. We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebras (for example all the Hopf algebras). As a first application we show that the Hochschild-Serre identity is the dual statement of our result. In particular, we extend this identity to Hopf algebras. Secondly, we clarify the construction of a class of quasi-Hopf algebras.23 pages, 7 Postscript figures (uses epsfig.sty)Quantum Algebra16W30 (Primary) 17B37 (Secondary)text