The group of order preserving automorphisms of the ring of differential operators on a Laurent polynomial algebra in prime characteristic
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Abstract:
Let $K$ be a field of characteristic $p>0$. It is proved that the group $\mathrm {Aut}_{ord}(\mathcal {D}(L_n))$ of order preserving automorphisms of the ring $\mathcal {D}(L_n)$ of differential operators on a Laurent polynomial algebra $L_n:= K[x_1^{\pm 1}, \ldots , x_n^{\pm 1}]$ is isomorphic to a skew direct product of groups ${\mathbb {Z}}_p^n \rtimes \mathrm {Aut}_K(L_n)$, where ${\mathbb {Z}}_p$ is the ring of $p$-adic integers. Moreover, the group $\mathrm {Aut}_{ord}(\mathcal {D}(L_n))$ is found explicitly. Similarly, $\mathrm {Aut}_{ord}(\mathcal {D}(P_n))\simeq \mathrm {Aut}_K(P_n)$, where $P_n: =K[x_1, \ldots , x_n]$ is a polynomial algebra.References
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Additional Information
- V. V. Bavula
- Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
- MR Author ID: 293812
- Email: v.bavula@sheffield.ac.uk
- Received by editor(s): June 4, 2008
- Published electronically: January 26, 2009
- Communicated by: Martin Lorenz
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 1891-1898
- MSC (2000): Primary 16W20, 13N10, 16S32
- DOI: https://doi.org/10.1090/S0002-9939-09-09825-6
- MathSciNet review: 2480268