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

2005/12/10 by V. V. Bavula, Bavula, V. V. · 2 citations
Mathematics · Physics and Astronomy · #13N10 #13N15 #14H37 #14R15 #16S32 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0512215

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

Abstract

The inversion formula is given for automorphisms of the Weyl algebras with polynomial coefficients over a field of characteristic zero. The theorem of Gabber on the degree of polynomial automorphism is extended. It is proved that any automorphism of the Weyl algebra with polynomial coefficients is determined by its left (right) faces (extending the result of J. H. McKay and S. S.-S. Wang for polynomial automorphisms).

Citations

• An inversion formula for two polynomials in two variables

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