The Freiheitssatz for Poisson algebras
Leonid Makar-Limanov, Ualbai Umirbaev
TL;DR
This paper proves the Freiheitssatz for Poisson algebras over characteristic zero, explores automorphism tameness, and links the Jacobian conjecture to the Freiheitssatz via algebraic analogues.
Contribution
It establishes the Freiheitssatz for Poisson algebras and connects classical conjectures to algebraic properties using this result.
Findings
Freiheitssatz proven for Poisson algebras in characteristic zero
Automorphisms of two-generated free Poisson algebras are tame
Jacobian conjecture relates to an analogue of the commutator test theorem
Abstract
We prove the Freiheitssatz for Poisson algebras in characteristic zero. We also give a proof of the tameness of automorphisms for two generated free Poisson algebras and prove that an analogue of the commutator test theorem is equivalent to the two dimensional classical Jacobian conjecture using the Freiheitssatz and Jung's Theorem.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra · Nonlinear Waves and Solitons