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

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

2006-04-21

arxiv.org/abs/math/0604477v1

Mathematics

Rings and Algebras

29 pages

Scientific paper

Let $K$ be an {\em arbitrary} field of characteristic $p>0$, let $A$ be one of the following algebras: $P_n:= K[x_1, ..., x_n]$ 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 $K[[x_1, ..., x_n]]$, $T_{k_1, ..., k_n}$ is the subalgebra of $\CD (P_n)$ generated by $P_n$ and the higher derivations $\der_i^{[j]}$, $0\leq j

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