The inversion formulae for automorphisms of polynomial algebras and differential operators in prime characteristic
نویسنده
چکیده
Let K be an arbitrary field of characteristic p > 0, let A be one of the following algebras: Pn := K[x1, . . . , xn] is a polynomial algebra, D(Pn) is the ring of differential operators on Pn, D(Pn) ⊗ Pm, the n’th Weyl algebra An, the n’th Weyl algebra An ⊗ Pm with polynomial coefficients Pm, the power series algebra K[[x1, . . . , xn]], Tk1,...,kn is the subalgebra of D(Pn) generated by Pn and the higher derivations ∂ [j] i , 0 ≤ j < pi , i = 1, . . . , n (where k1, . . . , kn ∈ N), Tk1,...,kn ⊗ Pm, an arbitrary central simple (countably generated) algebra over an arbitrary field. The inversion formula for automorphisms of the algebra A is found explicitly. Mathematics subject classification 2000: 13N10, 13N15, 14R15, 14H37, 16S32.
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