POISSON BRACKETS DETERMINED BY JACOBIANS

DOI QR코드

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Ahn, Jaehyun;Oh, Sei-Qwon;Park, Sujin

  • 투고 : 2013.01.24
  • 심사 : 2013.04.04
  • 발행 : 2013.05.15

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.

키워드

Poisson bracket;Jacobian matrix;polynomial algebra

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.

과제정보

연구 과제 주관 기관 : Chungnam National University