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

Autor(es)

Makar-Limanov, Leonid ^{[1, 2, 3]} ; Shestakov, Ivan ^[4]

Afiliação do(s) autor(es)

^[1] Wayne State Univ, Dept Math, Detroit, MI 48202 - USA

^[2] Weizmann Inst Sci, Dept Math & Comp Sci, IL-76100 Rehovot - Israel

^[3] Univ Michigan, Dept Math, Ann Arbor, MI 48109 - USA

^[4] Univ Sao Paulo, Inst Math & Stat, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 349, n. 1, p. 372-379, JAN 1 2012.
• Citações Web of Science: 11

Resumo

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]). (C) 2011 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 06/59114-1 - Leonid Makar Limanov | Wayne State University - Estados Unidos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional