= Formal associative deformation
{title2=$a*b$}
= Formal deformation of an associative algebra
{synonym}
= Star product
{synonym}
A formal associative deformation is a unital $k[[t]]$-bilinear product continuous for the <adic topology> on $A[[t]]$ of the form $a*b=ab+\sum_{r\geq1}t^r\mu_r(a,b)$. Each coefficient $\mu_r$ is a $k$-bilinear map $A\otimes A\to A$, and the whole product satisfies <associativity>. For an infinite-dimensional <algebra>, $A[[t]]$ is the completed <tensor product> $\varprojlim_nA\otimes k[t]/(t^n)$ and generally differs from the ordinary $A\otimes k[[t]]$.
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