Restricted polynomial extensions
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초록
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.
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.
참고문헌 (14)
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