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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The group of order preserving automorphisms of the ring of differential operators on a Laurent polynomial algebra in prime characteristic
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by V. V. Bavula PDF
Proc. Amer. Math. Soc. 137 (2009), 1891-1898 Request permission

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