Characteristic free Galois rings and generalized Weyl algebras
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908768814497792 |
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| author | Schwarz, Joao |
| author_facet | Schwarz, Joao |
| contents | This paper develops from scratch a theory of Galois rings and orders over arbitrary fields. Our approach is different from others in the literature in that there is no non-modularity assumption. We prove, when the field is algebraically closed, the analogue of the Main Theorem of the representation theory of Galois orders by V. Futorny and S. Ovsienko. Then we develop a theory of infinite rank generalized Weyl algebras, which was never explicitly introduced in the literature before, and prove its basic properties. We expect their representation theory to be of interest for future works. Finally we show that under very mild assumptions, the invariants of generalized Weyl algebras under the action of non-exceptional irreducible complex reflection groups are a principal Galois orders, greatly generalizing, in an elementary fashion, results obtained previously for the Weyl algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characteristic free Galois rings and generalized Weyl algebras Schwarz, Joao Representation Theory Primary: 16G99 16W22 Secondary: 16P40 16S85 This paper develops from scratch a theory of Galois rings and orders over arbitrary fields. Our approach is different from others in the literature in that there is no non-modularity assumption. We prove, when the field is algebraically closed, the analogue of the Main Theorem of the representation theory of Galois orders by V. Futorny and S. Ovsienko. Then we develop a theory of infinite rank generalized Weyl algebras, which was never explicitly introduced in the literature before, and prove its basic properties. We expect their representation theory to be of interest for future works. Finally we show that under very mild assumptions, the invariants of generalized Weyl algebras under the action of non-exceptional irreducible complex reflection groups are a principal Galois orders, greatly generalizing, in an elementary fashion, results obtained previously for the Weyl algebras. |
| title | Characteristic free Galois rings and generalized Weyl algebras |
| topic | Representation Theory Primary: 16G99 16W22 Secondary: 16P40 16S85 |
| url | https://arxiv.org/abs/2601.10346 |