Poisson brackets on some skew PBW extensions

Abstract

In [1] the author gives a description of Poisson brackets on some algebras of quantum polynomials Oq, 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 Oʳ,ⁿq,δ , which are generalization of Oq, and show some examples of skew PBW extension where we can apply this description.