Assume is the free Poisson algebra on the set of generators $=\{_{1},_{2},…,_{}\}$. It is well-known that is the polynomial algebra with infinitely many generators $y_{1}$, $y_{2}$, ... where $_{1}=_{1}$,…,$_{}=_{}$,$_{+1}=[_{1},_{2}]$,... is a basis of the free Lie algebra on and [-,-] denotes the Lie bracket on this free Lie algebra. What is the quotient of by the Poisson ideal generated by the set $\{_{1},_{2},...,_{n}\}$?
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