the statement is:
given $f,g \in C^{\infty}(M)$ the it's true that $\xi_{\{f,g\}}=[\xi_{f},\xi_{g}]$
M should be a symplectic poisson manifold
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You might want to give a little more info. so people understand what you are asking. – copper.hat Oct 02 '18 at 16:24
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@copper.hat I'm at the lecture now, the lecturer even doesn't know. not that it is too complicated the lecturer dosen't know what he is doing. typical of classes in russia actually – kristenA Oct 02 '18 at 16:26
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Is ${f,g}$ the Poisson bracket, while $[\xi_{f},\xi_{g}]$ is the Lie bracket? – Paul Sinclair Oct 02 '18 at 23:03
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@PaulSinclair sounds like it is – kristenA Oct 03 '18 at 07:20