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arXiv · 2601.23110

Lifts of endomorphisms of Weyl algebras modulo $p^2$

Niels Lauritzen·Jesper Funch Thomsen
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Abstract

Let $\varphi$ denote a $k$-algebra endomorphism of the $n$-th Weyl algebra $A_n(k)$ over a perfect field $k$ of positive characteristic $p$. We prove that $\varphi$ can be lifted to an endomorphism of the Weyl algebra $A_n(W_2(k))$ over the Witt vectors $W_2(k)$ of length two over $k$ if and only if $\varphi$ induces a Poisson morphism of the center of $A_n(k)$. Furthermore, we improve a result of Tsuchimoto, which enables us to conclude that these equivalent statements hold at least when ${\rm deg}(\varphi) < p$. In particular, we conclude that $\varphi$ is injective if ${\rm deg}(\varphi) < p$.

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BibTeXRIS

Niels Lauritzen, Jesper Funch Thomsen. 2026-01-30. Lifts of endomorphisms of Weyl algebras modulo $p^2$. https://arxiv.org/abs/2601.23110

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