The size of a stratifying system can be arbitrarily large
In this short note we construct two families of examples of large stratifying systems in module categories of algebras. The first examples consist on stratifying systems of infinite size in the module category of an algebra $A$. In the second family of examples we show that the size of a finite stra...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.385/ |
| _version_ | 1797651482653229056 |
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| author | Treffinger, Hipolito |
| author_facet | Treffinger, Hipolito |
| author_sort | Treffinger, Hipolito |
| collection | DOAJ |
| description | In this short note we construct two families of examples of large stratifying systems in module categories of algebras. The first examples consist on stratifying systems of infinite size in the module category of an algebra $A$. In the second family of examples we show that the size of a finite stratifying system in the module category of a finite dimensional algebra $A$ can be arbitrarily large in comparison to the number of isomorphism classes of simple $A$-modules. We note that both families of examples are built using well-established results in higher homological algebra. |
| first_indexed | 2024-03-11T16:16:26Z |
| format | Article |
| id | doaj.art-949df68cebf34598bde91f0a9f88916d |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:26Z |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-949df68cebf34598bde91f0a9f88916d2023-10-24T14:20:20ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G1151910.5802/crmath.38510.5802/crmath.385The size of a stratifying system can be arbitrarily largeTreffinger, Hipolito0Institut de Mathématiques Jussieu - Paris Rive Gauge, Université Paris Cité. Paris, FranceIn this short note we construct two families of examples of large stratifying systems in module categories of algebras. The first examples consist on stratifying systems of infinite size in the module category of an algebra $A$. In the second family of examples we show that the size of a finite stratifying system in the module category of a finite dimensional algebra $A$ can be arbitrarily large in comparison to the number of isomorphism classes of simple $A$-modules. We note that both families of examples are built using well-established results in higher homological algebra.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.385/ |
| spellingShingle | Treffinger, Hipolito The size of a stratifying system can be arbitrarily large Comptes Rendus. Mathématique |
| title | The size of a stratifying system can be arbitrarily large |
| title_full | The size of a stratifying system can be arbitrarily large |
| title_fullStr | The size of a stratifying system can be arbitrarily large |
| title_full_unstemmed | The size of a stratifying system can be arbitrarily large |
| title_short | The size of a stratifying system can be arbitrarily large |
| title_sort | size of a stratifying system can be arbitrarily large |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.385/ |
| work_keys_str_mv | AT treffingerhipolito thesizeofastratifyingsystemcanbearbitrarilylarge AT treffingerhipolito sizeofastratifyingsystemcanbearbitrarilylarge |