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 Restricted polynomial extensions Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 865-876 https://doi.org/10.4134/BKMS.b200590Published online June 25, 2021Printed July 31, 2021 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. Keywords : Skew polynomial algebra (Ore extension), Poisson algebra, quantization, semiclassical limit MSC numbers : 16S36, 17B63 Supported by : The second author is supported by Chungnam Nationality University Grant. Downloads: Full-text PDF   Full-text HTML