Poisson brackets on some skew PBW extensions

In [1] the author gives a description of Poisson brackets on some algebras of quantum polynomials $\mathcal{O}_q$, which is called the general algebra of quantum polynomials. The main of this paper is to present a generalization of [1] through a description of Poisson brackets on some skew PBW extensions of a ring $A$ by the extensions $\mathcal{O}_{q,\delta}^{r,n}$, which are generalization of $\mathcal{O}_q$, and show some examples of skew PBW extension where we can apply this description.