충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권2호
  • /
  • Pages.357-365
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  • 2013
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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POISSON BRACKETS DETERMINED BY JACOBIANS

  • Ahn, Jaehyun (Department of Mathematics Chungnam National University) ;
  • Oh, Sei-Qwon (Department of Mathematics Chungnam University) ;
  • Park, Sujin (Department of Mathematics Chungnam University)
  • 투고 : 2013.01.24
  • 심사 : 2013.04.04
  • 발행 : 2013.05.15
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초록

Fix $n-2$ elements $h_1,{\cdots},h_{n-2}$ of the quotient field B of the polynomial algebra $\mathbb{C}[x_1,x_2,{\cdots},x_n]$. It is proved that B is a Poisson algebra with Poisson bracket defined by $\{f,g\}=det(Jac(f,g,h_1,{\cdots},h_{n-2})$ for any $f,g{\in}B$, where det(Jac) is the determinant of a Jacobian matrix.

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참고문헌

  1. D. A. Jordan and S. Oh, Poisson brackets and Poisson spectra in polynomial algebras, New Trends in Noncommutative Algebra, Contemp. Math. 562 (2012), 169-187. https://doi.org/10.1090/conm/562/11136
  2. D. A. Jordan and S. Oh, Poisson spectra in polynomial algebras, arXiv:math.RA/1212.5158 (2012).
  3. A. N. Panov, n-Poisson and n-Sklyanin brackets, Journal of Mathematical Sciences 110 (2002), 2322-2329. https://doi.org/10.1023/A:1014953924173
  4. R. Przybysza, On one class of exact Poisson structures, Journal of Mathematical Physics 424 (2001), no. 4, 1913-1920.