2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79220We construct a differential and a Lie bracket on the space\linebreak $\{\Hom (A^{\otimes k}, A^{\otimes l})\},_{k,l\ge 0}$ for any associative algebra $A$. The restriction of this bracket to the space $\{\Hom (A^{\otimes k}, A)\},_{k\ge 0}$ is exactly the Gerstenhaber bracket. We discuss some formality conjecture related with this construction. We also discuss some applications to deformation theory.4 pages, 1 figureQuantum Algebratext