Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields

We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automor...

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 2012, Vol.349 (1), p.372-379
Main Authors: Makar-Limanov, Leonid, Shestakov, Ivan
Format: Article
Language:English
Subjects:
Free Poisson algebras
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that any two Poisson dependent elements in a free Poisson algebra and a free Poisson field of characteristic zero are algebraically dependent, thus answering positively a question from Makar-Limanov and Umirbaev (2007) [8]. We apply this result to give a new proof of the tameness of automorphisms for free Poisson algebras of rank two (see Makar-Limanov and Umirbaev (2011) [9], Makar-Limanov et al. (2009) [10]).
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2011.08.008