  In a classic paper, Gerstenhaber showed that first order deformations of an
associative k-algebra A are controlled by the second Hochschild cohomology
group of A. More generally, any n-parameter first order deformation of A gives,
due to commutativity of the cup-product on Hochschild cohomology, a morphism
from the graded algebra Sym(k^n) to Ext^*(A,A), the Ext-algebra in the category
of A-bimodules.
  We prove that any extension of the n-parameter first order deformation of A
to an INFINITE ORDER formal deformation provides a canonical `lift' of the
graded algebra morphism above to a dg-algebra morphism from Sym(k^n) to the
dg-algebra RHom(A,A), where the Symmetric algebra Sym(k^n) is viewed as a
dg-algebra (generated by the vector space $\k^n$ placed in degree 2) with zero
differential.
