A Dixmier theorem for Poisson enveloping algebras

Ualbai Umirbaev, Viktor Zhelyabin

We consider a skew-symmetric $n$-ary bracket on the polynomial algebra $K[x_1,\dots ,x_n,x_{n+1}]$ ($n\ge 2$) over a field $K$ of characteristic zero defined by $\{a_1,\ldots,a_n\…