The Freiheitssatz for Poisson algebras

We prove the Freiheitssatz for Poisson algebras in characteristic zero. We also give a new proof of the tameness of automorphisms for two generated free Poisson algebras and show that an analogue of the commutator test theorem is equivalent to the two-dimensional classical Jacobian conjecture.

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Bibliographic Details
Published in:Journal of algebra 2011-02, Vol.328 (1), p.495-503
Main Authors: Makar-Limanov, Leonid, Umirbaev, Ualbai
Format: Article
Language:English
Subjects:
Automorphisms
Freiheitssatz
Poisson algebras
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Description
Summary:We prove the Freiheitssatz for Poisson algebras in characteristic zero. We also give a new proof of the tameness of automorphisms for two generated free Poisson algebras and show that an analogue of the commutator test theorem is equivalent to the two-dimensional classical Jacobian conjecture.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2010.08.015