On the category $\mathcal{O}$ for generalized Weyl algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915195412021248 |
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| author | Velasco, Ruben Mamani Tikaradze, Akaki |
| author_facet | Velasco, Ruben Mamani Tikaradze, Akaki |
| 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 $\mathbb{Z}/p^n\mathbb{Z}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the category $\mathcal{O}$ for generalized Weyl algebras Velasco, Ruben Mamani Tikaradze, Akaki Quantum Algebra 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 $\mathbb{Z}/p^n\mathbb{Z}.$ |
| title | On the category $\mathcal{O}$ for generalized Weyl algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2503.09921 |