Gerstenhaber deformation

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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]].