Abstract
ABSTRACTThe 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 of a free GP-field is a free ideal ring. Besides, the Poisson and polynomial dependence of two elements are equivalent in . 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}≅Aut P{x,y}≅Aut k[x,y].
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