  Universal Deformation Formulas (UDFs) for the deformation of associative
algebras play a key role in deformation quantization. Here we present examples
for certain classes of infinitesimals. A basic representable 2-cocycle $F$ of
an associative algebra $\mathcal A$ is one for which there exist commuting
derivations $D,\dots, D_n$ of $\mathcal A$ such that $F = \sum_{ij}a_{ij}D_i
\smile D_j$, where the $a_{ij}$ are central elements of $\mathcal A$. When
$\mathcal A$ is defined over the rationals, there is a natural definition of
the exponential of such a cocycle. With this $\exp \hbar F$ defines a formal
one-parameter family of deformations of $\mathcal A$, where $\hbar$ is a
deformation parameter. The rational quantization of smooth functions on a
smooth manifold using a bivector field as an infinitesimal deformation is a
special case.
