The group of order preserving automorphisms of the ring of differential operators on Laurent polynomial algebra in prime characteristic

Details The group of order preserving automorphisms of the ring of differential operators on Laurent polynomial algebra in prime characteristic The group of order preserving automorphisms of the ring of differential operators on Laurent polynomial algebra in prime characteristic

2008-06-05

arxiv.org/abs/0806.1038v1

Mathematics

Rings and Algebras

8 pages

Scientific paper

Let $K$ be a field of characteristic $p>0$. It is proved that the group $\Aut_{ord}(\CD (L_n))$ of order preserving automorphisms of the ring $\CD (L_n)$ of differential operators on a Laurent polynomial algebra $L_n:= K[x_1^{\pm 1}, ..., x_n^{\pm 1}]$ is isomorphic to a skew direct product of groups $\Zp^n \rtimes \Aut_K(L_n)$ where $\Zp$ is the ring of $p$-adic integers. Moreover, the group $\Aut_{ord}(\CD (L_n))$ is found explicitly. Similarly, $\Aut_{ord}(\CDPn)\simeq \Aut_K(P_n)$ where $P_n: =K[x_1, ..., x_n]$ is a polynomial algebra.

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