 Formal associative deformation

A formal associative deformation is a unital $k[[t]]$-bilinear product continuous for the adic topology on $A[[t]]$ of the form $a\ast b=ab+{\sum }_{r\ge 1}{t}^r{\mu }_r(a,b)$. 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 ${\underleftarrow{\lim }}_{n}A\otimes k[t]/(t^n)$ and generally differs from the ordinary $A\otimes k[[t]]$.