POISSON BRACKETS DETERMINED BY JACOBIANS

Abstract

Fix n − 2 elements h1, · · · , hn−2 of the quotient field B of the polynomial algebra C[x1, x2, · · · , xn]. It is proved that B is a Poisson algebra with Poisson bracket defined by {f, g} = det(Jac(f, g, h1, · · · , hn−2)) for any f, g ∈ B, where det(Jac) is the determinant of a Jacobian matrix.

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