Free generic Poisson fields and algebras

Author(s)

Kaygorodov, Ivan ^[1] ; Shestakov, Ivan ^{[2, 3]} ; Umirbaev, Ualbai ^[4]

Affiliation

^[1] Univ Fed ABC, Sao Paulo - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

^[3] Soboley Inst Math, Novosibirsk - Russia

^[4] Wayne State Univ, Detroit, MI - USA

• Document type: Journal article
• Source: COMMUNICATIONS IN ALGEBRA; v. 46, n. 4, p. 1799-1812, 2018.
• Web of Science Citations: 1

Abstract

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]. (AU)

• FAPESP's process: 14/24519-8 - Generalized derivations of non associative algebras and superalgebras
• Grantee: Ivan Kaygorodov
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants