On a theorem of B. Keller on Yoneda algebras of simple modules
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916546235858944 |
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| author | Jasso, Gustavo |
| author_facet | Jasso, Gustavo |
| contents | A theorem of Keller states that the Yoneda algebra of the simple modules over a finite-dimensional algebra is generated in cohomological degrees $0$ and $1$ as a minimal $A_\infty$-algebra. We provide a proof of an extension of Keller's theorem to abelian length categories by reducing the problem to a particular class of Nakayama algebras, where the claim can be shown by direct computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a theorem of B. Keller on Yoneda algebras of simple modules Jasso, Gustavo Representation Theory A theorem of Keller states that the Yoneda algebra of the simple modules over a finite-dimensional algebra is generated in cohomological degrees $0$ and $1$ as a minimal $A_\infty$-algebra. We provide a proof of an extension of Keller's theorem to abelian length categories by reducing the problem to a particular class of Nakayama algebras, where the claim can be shown by direct computation. |
| title | On a theorem of B. Keller on Yoneda algebras of simple modules |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2402.14004 |