Finitely generated bimodules over Weyl algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929246257020928 |
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| author | Lauritzen, Niels Thomsen, Jesper Funch |
| author_facet | Lauritzen, Niels Thomsen, Jesper Funch |
| contents | Let $A$ be the $n$-th Weyl algebra over a field of characteristic zero, and $φ:A\rightarrow A$ an endomorphism with $S = φ(A)$. We prove that if $A$ is finitely generated as a left or right $S$-module, then $S = A$. The proof involves reduction to large positive characteristics. By holonomicity, $A$ is always finitely generated as an $S$-bimodule. Moreover, if this bimodule property could be transferred into a similar property in large positive characteristics, then we could again conclude that $A=S$. The latter would imply the Dixmier Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09384 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finitely generated bimodules over Weyl algebras Lauritzen, Niels Thomsen, Jesper Funch Algebraic Geometry Rings and Algebras 14A22, 14R10, 16H05 Let $A$ be the $n$-th Weyl algebra over a field of characteristic zero, and $φ:A\rightarrow A$ an endomorphism with $S = φ(A)$. We prove that if $A$ is finitely generated as a left or right $S$-module, then $S = A$. The proof involves reduction to large positive characteristics. By holonomicity, $A$ is always finitely generated as an $S$-bimodule. Moreover, if this bimodule property could be transferred into a similar property in large positive characteristics, then we could again conclude that $A=S$. The latter would imply the Dixmier Conjecture. |
| title | Finitely generated bimodules over Weyl algebras |
| topic | Algebraic Geometry Rings and Algebras 14A22, 14R10, 16H05 |
| url | https://arxiv.org/abs/2308.09384 |