= Poisson bracket from a central deformation parameter
{c}
{title2=$\{\bar a,\bar b\}=h^{-1}[a,b]\bmod h$}
Let $h$ be central and a non-zero-divisor in an associative algebra, with commutative quotient modulo $h$. Dividing commutators by $h$ and reducing modulo $h$ is independent of the lifts, since changing a lift by $hc$ changes the quotient by a commutator, zero modulo $h$. Antisymmetry, the Leibniz rule and the Jacobi identity descend from the corresponding commutator identities. For the <order filtration of a Weyl algebra>, the convention is $\{\xi_i,x_j\}=\delta_{ij}$, with the opposite sign for $\{x_i,\xi_j\}$.
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