2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79197The associator of a non-associative algebra is the curvature of the Hochschild quasi-complex. The relationship ``curvature-associator'' is investigated. Based on this generic example, we extend the geometric language of vector fields to a purely algebraic setting, similar to the context of Gerstenhaber algebras. We interprete the elements of a non-associative algebra with a Lie bracket as ``vector fields'' and the multiplication as a connection. We investigate conditions for the existance of an ``algebra of functions'' having as algebra of derivations the original non-associative algebra.AMS-LaTex, 15 pagesDifferential GeometryQuantum Algebra58A12, 14A22 (Primary) 17A75 (Secondary)text