충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제31권1호
  • /
  • Pages.47-52
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  • 2018
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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A NATURAL MAP ON AN ORE EXTENSION

  • Cho, Eun-Hee (Department of Mathematics Chungnam National University) ;
  • Oh, Sei-Qwon (Department of Mathematics Chungnam National University)
  • 투고 : 2017.10.03
  • 심사 : 2017.12.01
  • 발행 : 2018.02.15
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초록

Let ${\delta}$ be a derivation in a noetherian integral domain A. It is shown that a natural map induces a homeomorphism between the spectrum of $A[z;{\delta}]$ and the Poisson spectrum of $A[z;{\delta}]_p$ such that its restriction to the primitive spectrum of $A[z;{\delta}]$ is also a homeomorphism onto the Poisson primitive spectrum of $A[z;{\delta}]_p$.

키워드

참고문헌

  1. E.-H. Cho and S.-Q. Oh, Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra, Letters in Math. Phys. 106 (2016), no. 7, 997-1009.
  2. K. R. Goodearl and R. B. Warfield, An introduction to noncommutative noetherian rings, London Mathematical Society Student Text 16, Cambridge University Press, 1989.
  3. D. A. Jordan, Ore extensions and Poisson algebras, Glasgow Math. J. 56 (2014), no. 2, 355-368. https://doi.org/10.1017/S0017089513000293
  4. A. P. Kitchin and S. Launois, Endomorphisms of quantum generalized Weyl algebras, Letters in Math. Phys. 104 (2014), 837-848.
  5. N.-H. Myung and S.-Q. Oh, Automorphism groups of Weyl algebras, arXiv.org: [math.RA] (2017).
  6. S.-Q. Oh, Poisson polynomial rings, Comm. Algebra, 34 (2006), 1265-1277.
  7. S.-Q. Oh, Poisson prime ideals of Poisson polynomial rings, Comm. Algebra, 35 (2007), 3007-3012.
  8. S.-Q. Oh, Quantum and Poisson structures of multi-parameter symplectic and Euclidean spaces, J. Algebra, 319 (2008), 4485-4535.
  9. S.-Q. Oh, A natural map from a quantized space onto its semiclassical limit and a multi-parameter Poisson Weyl algebra, Comm. Algebra, 45 (2017), 60-75.
  10. S.-Q. Oh and M.-Y. Park, Relationship between quantum and Poisson structures of odd dimensional Euclidean spaces, Comm. Algebra, 38 (2010), no. 9, 3333-3346. https://doi.org/10.1080/00927870903114987