Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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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)
  • Received : 2013.01.24
  • Accepted : 2013.04.04
  • Published : 2013.05.15
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Abstract

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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References

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