Free generic Poisson fields and algebras

The free generic Poisson algebras (GP-algebras) over a field k of characteristic 0 are studied. We prove that certain properties of free Poisson algebras are true for free GP-algebras as well. In particular, the universal multiplicative enveloping algebra U = U(GP(x(1), . . . , x(n))) of a free GP-field GP(x(1), . . . , x(n)) is a free ideal ring. Besides, the Poisson and polynomial dependence of two elements are equivalent in GP(x(1), . . . , x(n)). As a corollary, all automorphisms of the free GP-algebra GP{x, y} are tame and we have the isomorphisms of groups of automorphisms Aut GP{x, y} congruent to Aut P{x, y} congruent to Aut k[x, y].