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 [Formula omitted.] of a free GP-field [Formu...

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Bibliographic Details
Published in:Communications in algebra 2018-04, Vol.46 (4), p.1799-1812
Main Authors: Kaygorodov, Ivan, Shestakov, Ivan, Umirbaev, Ualbai
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Isomorphism
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Summary: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 [Formula omitted.] of a free GP-field [Formula omitted.] is a free ideal ring. Besides, the Poisson and polynomial dependence of two elements are equivalent in [Formula omitted.] . 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}[approx equal to]Aut P{x,y}[approx equal to]Aut k[x,y].
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2017.1358269