Advances in Mathematics· 2026Q1
Lifts of endomorphisms of Weyl algebras modulo p2
- 0citations
- Q1SCImago
- 2026year
Short summary
Endomorphisms of Weyl algebras over fields of positive characteristic p can be lifted to a larger ring if and only if they preserve the Poisson structure of the algebra's center.
AI-generated from the title and abstract; the full text is not read.
Key points
- An endomorphism φ of the n-th Weyl algebra A_n(k) over a field k of positive characteristic p can be lifted to A_n(W_2(k)) if and only if it induces a Poisson morphism on the center of A_n(k).
- This equivalence holds when the degree of φ is less than p.
- When deg(φ) < p, the endomorphism φ is necessarily injective.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let φ 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 φ 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 φ 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 deg ( φ ) < p . In particular, we conclude that φ is injective if deg ( φ ) < p .
The authors' abstract, as published at the source. Advances in Mathematics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Algebra and Number Theory
Algebra and Number TheoryMathematics