Gerstenhaber deformation

Definition

Let $A$ be an algebra (not necessarily associative) over a field $k$. Then, a Gerstenhaber deformation of $A$ is defined as an algebra ${\tilde {A}}$ over the ring $K[[\nu ]]$ (ring of formal power series in the formal variable $\nu$), such that ${\tilde {A}}/\nu {\tilde {A}}\simeq A$. Two Gerstenhaber deformations are termed equivalent if they are isomorphic over $K[[\nu ]]$ and a Gerstenhaber deformation is trivial if it is obtained by extending the base ring from $K$ to $K[[\nu ]]$.