Extensions of the Frobenius to the ring of differential operators on a polynomial algebra in prime characteristic
Author:
V. V. Bavula
Journal:
Trans. Amer. Math. Soc. 363 (2011), 417437
MSC (2000):
Primary 13A35, 13N10, 16S32, 16W20, 16W22
Published electronically:
August 27, 2010
MathSciNet review:
2719688
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Abstract: Let be a field of characteristic . It is proved that each automorphism of the ring of differential operators on a polynomial algebra is uniquely determined by the elements , and that the set of all the extensions of the Frobenius (homomorphism) from certain maximal commutative polynomial subalgebras of , such as , to the ring is equal to where is the set of all the extensions of the Frobenius from to that leave invariant the subalgebra of scalar differential operators. The set is found explicitly; it is large (a typical extension depends on countably many independent parameters).
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Additional Information
V. V. Bavula
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email:
v.bavula@sheffield.ac.uk
DOI:
http://dx.doi.org/10.1090/S000299472010050998
Keywords:
Extensions of the Frobenius,
ring of differential operators,
Frobenius polynomial subalgebra,
group of automorphisms
Received by editor(s):
August 21, 2008
Received by editor(s) in revised form:
May 3, 2009
Published electronically:
August 27, 2010
Article copyright:
© Copyright 2010
American Mathematical Society
