The size of a stratifying system can be arbitrarily large

Hipolito Treffinger

doi:10.5802/crmath.385

Algèbre, Théorie des représentations

The size of a stratifying system can be arbitrarily large

Hipolito Treffinger ¹

¹ Institut de Mathématiques Jussieu - Paris Rive Gauge, Université Paris Cité. Paris, France

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 15-19.

Résumé

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.

Reçu le : 2021-01-28
Révisé le : 2021-09-15
Accepté le : 2022-05-25
Publié le : 2023-01-12

DOI : 10.5802/crmath.385

Affiliations des auteurs :

Hipolito Treffinger ¹

¹ Institut de Mathématiques Jussieu - Paris Rive Gauge, Université Paris Cité. Paris, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Hipolito Treffinger},
     title = {The size of a stratifying system can be arbitrarily large},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {15--19},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.385},
     language = {en},
}

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Hipolito Treffinger. The size of a stratifying system can be arbitrarily large. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 15-19. doi : 10.5802/crmath.385. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.385/

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