The inversion formulae for automorphisms of polynomial algebras and rings of differential operators in prime characteristic |
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Authors: | VV Bavula |
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Institution: | Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK |
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Abstract: | Let K be an arbitrary field of characteristic p>0. We find an explicit formula for the inverse of any algebra automorphism of any of the following algebras: the polynomial algebra Pn?Kx1,…,xn], the ring of differential operators D(Pn) on Pn, D(Pn)⊗Pm, the n’th Weyl algebra An or An⊗Pm, the power series algebra Kx1,…,xn]], the subalgebra Tk1,…,kn of D(Pn) generated by Pn and the higher derivations , 0≤j<pki, i=1,…,n (where k1,…,kn∈N), Tk1,…,kn⊗Pm or an arbitrary central simple (countably generated) algebra over an arbitrary field. |
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Keywords: | 13N10 13N15 14R15 14H37 16S32 |
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