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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.09921 |
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Table of Contents:
- Let $H(R, ϕ, z)$ be a generalized Weyl algebra associated with a ring $R$, its central element $z\in Z(R)$ and an automorphism $ϕ,$ such that for some $l \geq 1$, $ϕ^l(z)-z$ is nilpotent and $(z,ϕ^i(z))=R$ for all $0<i<l$. We prove that the category $\mathcal{O}$ over $H(R, z,ϕ)$ is equivalent to the category $\mathcal{O}$ over its $l$-th twist the generalized Weyl algebra $H(R, z,ϕ^l).$ This result is significantly more general than the corresponding one for the Weyl algebra over $\mathbb{Z}/p^n\mathbb{Z}.$