A natural map from a quantized space onto its semiclassical limit

Let $\widehat{\mathrm{\Gamma }}$ be the natural map given in \cite[\S1]{Oh12}. Here, we construct a deformation $B_q$ of a Poisson algebra $B_1$ and a prime ideal $P$ of $B_q$ such that $\widehat{\mathrm{\Gamma }}(P)$ is not a Poisson prime ideal of $B_1$.