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Extriangulated ideal quotients, with applications to cluster theory and gentle algebras

Year: 2026
Type: article
Abstract: We extend results of Brüstle–Yang on ideal quotients of 2-term subcategories of perfect derived categories of non-positive dg algebras to a relative setting. We find a new interpretation of such quotients: they appear as prototypical examples of a new construction of quotients of extriangulated categories by ideals generated by morphisms from injectives to projectives. We apply our results to Frobenius exact cluster categories and Higgs categories with suitable relative extriangulated structures, and to categories of walks related to gentle algebras. In all three cases, the extriangulated structures are well-behaved (they are 0-Auslander) and their quotients are equivalent to homotopy categories of two-term complexes of projectives over suitable finite-dimensional algebras.
DOI: 10.1016/j.jpaa.2026.108370
Institutions: RWTH Aachen University, University of Vienna, Centre National de la Recherche Scientifique, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne, Université de Versailles Saint-Quentin-en-Yvelines, Université Paris-Saclay, Laboratoire de Mathématiques de Versailles, University of Glasgow
Language: English
Open Access status: hybrid
Estimated APC paid: $3,550
Funders: European Commission, Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche, Institut Universitaire de France, Hausdorff Center for Mathematics, Engineering and Physical Sciences Research Council, European Research Council, Division of Mathematical Sciences
Awards: G2203179303, Dimer models with boundary, G3010527862, G3341554066, G3659979002, G434337789, Isaac Newton Institute for Mathematical Sciences, Clusters, Homological Algebra, Representations and Mirror Symmetry
OpenAlex ID: W4385775071
FWCI: 14.28
Cites: 54
Cited by: 19
Related to: 10