Poisson spectra in polynomial algebras

A significant class of Poisson brackets on the polynomial algebra C[x1,…,xn]C[x1,…,xn] is studied and, for this class of Poisson brackets, the Poisson prime ideals, Poisson primitive ideals and symplectic cores are determined. Moreover it is established that these Poisson algebras satisfy the Poisson Dixmier–Moeglin equivalence.