No-Ho Myung, Sei-Qwon Oh Chungnam National University; Chungnam National University

Abstract : Let $\mathbb F$ be a commutative ring. A restricted skew polynomial extension over $\mathbb F$ is a class of iterated skew polynomial $\mathbb F$-algebras which include well-known quantized algebras such as the quantum algebra $U_q(\mathfrak{sl}_2)$, Weyl algebra, etc. Here we obtain a necessary and sufficient condition in order to be restricted skew polynomial extensions over $\mathbb F$. We also introduce a restricted Poisson polynomial extension which is a class of iterated Poisson polynomial algebras and observe that a restricted Poisson polynomial extension appears as semiclassical limits of restricted skew polynomial extensions. Moreover, we obtain usual as well as unusual quantized algebras of the same Poisson algebra as applications.