The \rm Jacobian Conjecture_2n implies the \rm Dixmier Problem_n

2005/12/12 by V. V. Bavula, Bavula, V. V.
Mathematics · Physics and Astronomy · #14H37 #14R15 #16S32 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0512250

openalex publication_date 2005/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the author's inversion formula for automorphisms of the Weyl algebras with polynomial coefficients and the bound on its degree a slightly shorter (algebraic) proof is given of the result of A. Belov-Kanel and M. Kontsevich that the Jacobian Conjecture implies the Dixmier Proplem. No originality is claimed.

Citations

• The inversion formula for automorphisms of the Weyl algebras and polynomial algebras

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