2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67358We develop the deformation theory of A_\infty algebras together with \infty inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A_\infty algebras, associative algebras with inner products, and A_\infty algebras with inner products.14 pagesQuantum Algebra55P10;16S10;16S80text