  The 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.
