Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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RESTRICTED POLYNOMIAL EXTENSIONS

  • Myung, No-Ho (Department of Mathematics Chungnam National University) ;
  • Oh, Sei-Qwon (Department of Mathematics Chungnam National University)
  • Received : 2020.07.09
  • Accepted : 2021.05.07
  • Published : 2021.07.31
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Abstract

Let 𝔽 be a commutative ring. A restricted skew polynomial extension over 𝔽 is a class of iterated skew polynomial 𝔽-algebras which include well-known quantized algebras such as the quantum algebra Uq(𝔰𝔩2), Weyl algebra, etc. Here we obtain a necessary and sufficient condition in order to be restricted skew polynomial extensions over 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.

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Acknowledgement

The second author is supported by Chungnam Nationality University Grant.

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