On a theorem of B. Keller on Yoneda algebras of simple modules
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 t...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.655/ |
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| author | Jasso, Gustavo |
| author_facet | Jasso, Gustavo |
| author_sort | Jasso, Gustavo |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-3b080f2c28664496b741ed8a65078986 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-3b080f2c28664496b741ed8a650789862025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111449145310.5802/crmath.65510.5802/crmath.655On a theorem of B. Keller on Yoneda algebras of simple modulesJasso, Gustavo0Lund University, Centre for Mathematical Sciences, Box 118, 22100 Lund, SwedenA 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 $-algebra. We provide a proof of an extension of Keller’s theorem to abelian length categories by reducing the problem to a particular class of Nakayama algebras, where the claim can be shown by direct computation.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.655/Yoneda algebrassimple modulesNakayama algebras$A_\infty $-algebras |
| spellingShingle | Jasso, Gustavo On a theorem of B. Keller on Yoneda algebras of simple modules Comptes Rendus. Mathématique Yoneda algebras simple modules Nakayama algebras $A_\infty $-algebras |
| title | On a theorem of B. Keller on Yoneda algebras of simple modules |
| title_full | On a theorem of B. Keller on Yoneda algebras of simple modules |
| title_fullStr | On a theorem of B. Keller on Yoneda algebras of simple modules |
| title_full_unstemmed | On a theorem of B. Keller on Yoneda algebras of simple modules |
| title_short | On a theorem of B. Keller on Yoneda algebras of simple modules |
| title_sort | on a theorem of b keller on yoneda algebras of simple modules |
| topic | Yoneda algebras simple modules Nakayama algebras $A_\infty $-algebras |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.655/ |
| work_keys_str_mv | AT jassogustavo onatheoremofbkelleronyonedaalgebrasofsimplemodules |