EXTENSIONS OF THE FROBENIUS TO THE RING OF DIFFERENTIAL OPERATORS ON A POLYNOMIAL ALGEBRA IN PRIME CHARACTERISTIC

作者：Bavula V V^*

来源：Transactions of the American Mathematical Society, 2011, 363(1): 417-437.

DOI：10.1090/S0002-9947-2010-05099-8

• Extensions of the Frobenius
• ring of differential operators
• Frobenius polynomial subalgebra
• group of automorphisms

Let K be a field of characteristic p > 0. It is proved that each automorphism sigma is an element of Aut(K) (D(P(n))) of the ring D(P(n)) of differential operators on a polynomial algebra P(n) = K[x(1), ..., x(n)] is uniquely determined by the elements sigma(x(1)), ..., sigma(x(n)), and that the set Frob(D(P(n))) of all the extensions of the Frobenius (homomorphism) from certain maximal commutative polynomial subalgebras of D(P(n)), such as P(n), to the ring D(P(n)) is equal to AutK(D(P(n))).F where F is the set of all the extensions of the Frobenius from P(n) to D(P(n)) 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).

• 出版日期2011-1