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Let us start with a review of deformation theory of associative algebras. Let A be an associative algebra over a field k of characteristic zero. Definition 1. A formal deformation of A is a k[[t]]-bilinear multiplication law mt: A[[t]] ⊗k[[t]] A[[t]] → A[[t]] on the space A[[t]] of formal power series in a variable t with coefficients in A, satisfying the following properties: mt(a, b) = a · b+m1(a, b)t+m2(a, b)t2 + · · · for a, b ∈ A, where a · b is the original multiplication on A, and mt is associative, which is equivalent to the equation mt(mt(a, b), c) = mt(a,mt(b, c)) for a, b, c ∈ A. Remark 2. Note that for a formal deformation mt of a commutative algebra A, the bracket defined by the first-order part of the commutator, {a, b}: =