A characterisation of higher torsion classes

Autores
August, Jenny; Haugland, Johanne; Jacobsen, Karin M.; Kvamme, Sondre; Palu, Yann; Treffinger Cienfuegos, Hipolito José
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let A be an abelian length category containing a d-cluster tilting subcategory M . We prove that a subcategory of M is a d-torsion class if and only if it is closed under d-extensions and d-quotients. This generalises an important result for classical torsion classes. As an application, we prove that the d-torsion classes in M form a complete lattice. Moreover, we use the characterisation to classify the d-torsion classes associated to higher Auslander algebras of type A , and give an algorithm to compute them explicitly. The classification is furthermore extended to the setup of higher Nakayama algebras.
Fil: August, Jenny. University of Glasgow; Reino Unido
Fil: Haugland, Johanne. Norwegian University of Science and Technology; Noruega
Fil: Jacobsen, Karin M.. University Aarhus; Dinamarca
Fil: Kvamme, Sondre. Norwegian University of Science and Technology; Noruega
Fil: Palu, Yann. Universite de Picardie Jules Verne (universite de Picardie Jules V);
Fil: Treffinger Cienfuegos, Hipolito José. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
TORSION CLASSES
D-ABELIAN CATEGORIES
TORSION THEORIES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/265642
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A characterisation of higher torsion classesAugust, JennyHaugland, JohanneJacobsen, Karin M.Kvamme, SondrePalu, YannTreffinger Cienfuegos, Hipolito JoséTORSION CLASSESD-ABELIAN CATEGORIESTORSION THEORIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A be an abelian length category containing a d-cluster tilting subcategory M . We prove that a subcategory of M is a d-torsion class if and only if it is closed under d-extensions and d-quotients. This generalises an important result for classical torsion classes. As an application, we prove that the d-torsion classes in M form a complete lattice. Moreover, we use the characterisation to classify the d-torsion classes associated to higher Auslander algebras of type A , and give an algorithm to compute them explicitly. The classification is furthermore extended to the setup of higher Nakayama algebras.Fil: August, Jenny. University of Glasgow; Reino UnidoFil: Haugland, Johanne. Norwegian University of Science and Technology; NoruegaFil: Jacobsen, Karin M.. University Aarhus; DinamarcaFil: Kvamme, Sondre. Norwegian University of Science and Technology; NoruegaFil: Palu, Yann. Universite de Picardie Jules Verne (universite de Picardie Jules V);Fil: Treffinger Cienfuegos, Hipolito José. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaCambridge University Press2025-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/265642August, Jenny; Haugland, Johanne; Jacobsen, Karin M.; Kvamme, Sondre; Palu, Yann; et al.; A characterisation of higher torsion classes; Cambridge University Press; Forum of Mathematics, Sigma; 13; 2-2025; 1-362050-5094CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/characterisation-of-higher-torsion-classes/FB7BBAC07301A6BE3663EA11A3DA476Binfo:eu-repo/semantics/altIdentifier/doi/10.1017/fms.2024.73info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:00:25Zoai:ri.conicet.gov.ar:11336/265642instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:00:25.682CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A characterisation of higher torsion classes
title A characterisation of higher torsion classes
spellingShingle A characterisation of higher torsion classes
August, Jenny
TORSION CLASSES
D-ABELIAN CATEGORIES
TORSION THEORIES
title_short A characterisation of higher torsion classes
title_full A characterisation of higher torsion classes
title_fullStr A characterisation of higher torsion classes
title_full_unstemmed A characterisation of higher torsion classes
title_sort A characterisation of higher torsion classes
dc.creator.none.fl_str_mv August, Jenny
Haugland, Johanne
Jacobsen, Karin M.
Kvamme, Sondre
Palu, Yann
Treffinger Cienfuegos, Hipolito José
author August, Jenny
author_facet August, Jenny
Haugland, Johanne
Jacobsen, Karin M.
Kvamme, Sondre
Palu, Yann
Treffinger Cienfuegos, Hipolito José
author_role author
author2 Haugland, Johanne
Jacobsen, Karin M.
Kvamme, Sondre
Palu, Yann
Treffinger Cienfuegos, Hipolito José
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv TORSION CLASSES
D-ABELIAN CATEGORIES
TORSION THEORIES
topic TORSION CLASSES
D-ABELIAN CATEGORIES
TORSION THEORIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let A be an abelian length category containing a d-cluster tilting subcategory M . We prove that a subcategory of M is a d-torsion class if and only if it is closed under d-extensions and d-quotients. This generalises an important result for classical torsion classes. As an application, we prove that the d-torsion classes in M form a complete lattice. Moreover, we use the characterisation to classify the d-torsion classes associated to higher Auslander algebras of type A , and give an algorithm to compute them explicitly. The classification is furthermore extended to the setup of higher Nakayama algebras.
Fil: August, Jenny. University of Glasgow; Reino Unido
Fil: Haugland, Johanne. Norwegian University of Science and Technology; Noruega
Fil: Jacobsen, Karin M.. University Aarhus; Dinamarca
Fil: Kvamme, Sondre. Norwegian University of Science and Technology; Noruega
Fil: Palu, Yann. Universite de Picardie Jules Verne (universite de Picardie Jules V);
Fil: Treffinger Cienfuegos, Hipolito José. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description Let A be an abelian length category containing a d-cluster tilting subcategory M . We prove that a subcategory of M is a d-torsion class if and only if it is closed under d-extensions and d-quotients. This generalises an important result for classical torsion classes. As an application, we prove that the d-torsion classes in M form a complete lattice. Moreover, we use the characterisation to classify the d-torsion classes associated to higher Auslander algebras of type A , and give an algorithm to compute them explicitly. The classification is furthermore extended to the setup of higher Nakayama algebras.
publishDate 2025
dc.date.none.fl_str_mv 2025-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/265642
August, Jenny; Haugland, Johanne; Jacobsen, Karin M.; Kvamme, Sondre; Palu, Yann; et al.; A characterisation of higher torsion classes; Cambridge University Press; Forum of Mathematics, Sigma; 13; 2-2025; 1-36
2050-5094
CONICET Digital
CONICET
url http://hdl.handle.net/11336/265642
identifier_str_mv August, Jenny; Haugland, Johanne; Jacobsen, Karin M.; Kvamme, Sondre; Palu, Yann; et al.; A characterisation of higher torsion classes; Cambridge University Press; Forum of Mathematics, Sigma; 13; 2-2025; 1-36
2050-5094
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/characterisation-of-higher-torsion-classes/FB7BBAC07301A6BE3663EA11A3DA476B
info:eu-repo/semantics/altIdentifier/doi/10.1017/fms.2024.73
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.493442

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