2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68641Let an n-algebra mean an algebra over the chain complex of the little n-cubes operad. We give a proof of Kontsevich's conjecture, which states that for a suitable notion of Hochschild cohomology in the category of n-algebras, the Hochschild cohomology complex of an n-algebra is an (n+1)-algebra. This generalizes a conjecture by Deligne for n=1, now proven by several authors.29 pages; final version, to appear in Compos. MathAlgebraic TopologyQuantum AlgebraRings and Algebras16E40, 18D50 (Primary) 17A30, 17A42, 18C15, 55P48 (Secondary)text