The inversion formulae for automorphisms of polynomial algebras and differential operators in prime characteristic

2006/04/21 by V. V. Bavula, Bavula, V. V. · 2 citations
Mathematics · Physics and Astronomy · #13N10 #13N15 #14H37 #14R15 #16S32 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0604477

openalex publication_date 2006/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be an \em arbitrary field of characteristic p>0, let A be one of the following algebras: P_n:= K[x₁, ..., x_n] is a polynomial algebra, \CD (P_n) is the ring of differential operators on P_n, \CD (P_n)\t P_m, the n'th \em Weyl algebra A_n, the n'th \em Weyl algebra A_n\t P_m with polynomial coefficients P_m, the power series algebra K[[x₁, ..., x_n]], T_{k1, ..., kn} is the subalgebra of \CD (P_n) generated by P_n and the higher derivations \der_i^[j], 0≤ j

Citations

• An inversion formula for two polynomials in two variables

Cited by

• An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators
• The group of order preserving automorphisms of the ring of differential operators on Laurent polynomial algebra in prime characteristic

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