Restricted polynomial extensions
Bull. Korean Math. Soc. 2021 Vol. 58, No. 4, 865-876
Published online June 25, 2021
Printed 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.
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