Extensions of the Frobenius to ring of differential operators on polynomial algebra in prime characteristic
نویسنده
چکیده
Let K be a field of characteristic p > 0. It is proved that each automorphism σ ∈ AutK(D(Pn)) of the ring D(Pn) of differential operators on a polynomial algebra Pn = K[x1, . . . , xn] is uniquely determined by the elements σ(x1), . . . , σ(xn), and the set Frob(D(Pn)) of all the extensions of the Frobenius from certain maximal commutative polynomial subalgebras of D(Pn), like Pn, is equal to AutK(D(Pn)) · F where F is the set of all the extensions of the Frobenius from Pn to D(Pn) that leave invariant the subalgebra of scalar differential operators. The set F is found explicitly, it is large (a typical extension depends on countably many independent parameters).
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