On tau-tilting subcategories

Autores
Asadollahi, Javad; Sadeghi, Somayeh; Treffinger Cienfuegos, Hipolito José
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The main theme of this paper is to study τ -tilting subcategories in an abelian category A with enough projective objects. We introduce the notion of τ -cotorsion torsion triples and investigate a bijection between the collection of τ -cotorsion torsion triples in A and the collection of support τ -tilting subcategories of A , generalizing the bijection by Bauer, Botnan, Oppermann, and Steen between the collection of cotorsion torsion triples and the collection of tilting subcategories of A . General definitions and results are exemplified using persistent modules. If A=Mod-R , where R is a unitary associative ring, we characterize all support τ -tilting (resp. all support τ− -tilting) subcategories of Mod-R in terms of finendo quasitilting (resp. quasicotilting) modules. As a result, it will be shown that every silting module (resp. every cosilting module) induces a support τ -tilting (resp. support τ− -tilting) subcategory of Mod-R . We also study the theory in Rep(Q,A) , where Q is a finite and acyclic quiver. In particular, we give an algorithm to construct support τ -tilting subcategories in Rep(Q,A) from certain support τ -tilting subcategories of A .
Fil: Asadollahi, Javad. University Of Isfahan; Irán
Fil: Sadeghi, Somayeh. University Of Isfahan; Irán
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
Materia
ABELIAN CATEGORY
(Τ-)TILTING SUBCATEGORY
TORSION THEORY
SILTING MODULE
QUIVER REPRESENTATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/235363
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On tau-tilting subcategoriesAsadollahi, JavadSadeghi, SomayehTreffinger Cienfuegos, Hipolito JoséABELIAN CATEGORY(Τ-)TILTING SUBCATEGORYTORSION THEORYSILTING MODULEQUIVER REPRESENTATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The main theme of this paper is to study τ -tilting subcategories in an abelian category A with enough projective objects. We introduce the notion of τ -cotorsion torsion triples and investigate a bijection between the collection of τ -cotorsion torsion triples in A and the collection of support τ -tilting subcategories of A , generalizing the bijection by Bauer, Botnan, Oppermann, and Steen between the collection of cotorsion torsion triples and the collection of tilting subcategories of A . General definitions and results are exemplified using persistent modules. If A=Mod-R , where R is a unitary associative ring, we characterize all support τ -tilting (resp. all support τ− -tilting) subcategories of Mod-R in terms of finendo quasitilting (resp. quasicotilting) modules. As a result, it will be shown that every silting module (resp. every cosilting module) induces a support τ -tilting (resp. support τ− -tilting) subcategory of Mod-R . We also study the theory in Rep(Q,A) , where Q is a finite and acyclic quiver. In particular, we give an algorithm to construct support τ -tilting subcategories in Rep(Q,A) from certain support τ -tilting subcategories of A .Fil: Asadollahi, Javad. University Of Isfahan; IránFil: Sadeghi, Somayeh. University Of Isfahan; IránFil: 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"; ArgentinaCanadian Mathematical Soc2024-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/235363Asadollahi, Javad; Sadeghi, Somayeh; Treffinger Cienfuegos, Hipolito José; On tau-tilting subcategories; Canadian Mathematical Soc; Canadian Journal Of Mathematics; 3-2024; 1-380008-414XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/product/identifier/S0008414X24000221/type/journal_articleinfo:eu-repo/semantics/altIdentifier/doi/10.4153/S0008414X24000221info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2207.00457info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:09:20Zoai:ri.conicet.gov.ar:11336/235363instacron: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:34982025-09-29 10:09:20.369CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On tau-tilting subcategories
title On tau-tilting subcategories
spellingShingle On tau-tilting subcategories
Asadollahi, Javad
ABELIAN CATEGORY
(Τ-)TILTING SUBCATEGORY
TORSION THEORY
SILTING MODULE
QUIVER REPRESENTATION
title_short On tau-tilting subcategories
title_full On tau-tilting subcategories
title_fullStr On tau-tilting subcategories
title_full_unstemmed On tau-tilting subcategories
title_sort On tau-tilting subcategories
dc.creator.none.fl_str_mv Asadollahi, Javad
Sadeghi, Somayeh
Treffinger Cienfuegos, Hipolito José
author Asadollahi, Javad
author_facet Asadollahi, Javad
Sadeghi, Somayeh
Treffinger Cienfuegos, Hipolito José
author_role author
author2 Sadeghi, Somayeh
Treffinger Cienfuegos, Hipolito José
author2_role author
author
dc.subject.none.fl_str_mv ABELIAN CATEGORY
(Τ-)TILTING SUBCATEGORY
TORSION THEORY
SILTING MODULE
QUIVER REPRESENTATION
topic ABELIAN CATEGORY
(Τ-)TILTING SUBCATEGORY
TORSION THEORY
SILTING MODULE
QUIVER REPRESENTATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The main theme of this paper is to study τ -tilting subcategories in an abelian category A with enough projective objects. We introduce the notion of τ -cotorsion torsion triples and investigate a bijection between the collection of τ -cotorsion torsion triples in A and the collection of support τ -tilting subcategories of A , generalizing the bijection by Bauer, Botnan, Oppermann, and Steen between the collection of cotorsion torsion triples and the collection of tilting subcategories of A . General definitions and results are exemplified using persistent modules. If A=Mod-R , where R is a unitary associative ring, we characterize all support τ -tilting (resp. all support τ− -tilting) subcategories of Mod-R in terms of finendo quasitilting (resp. quasicotilting) modules. As a result, it will be shown that every silting module (resp. every cosilting module) induces a support τ -tilting (resp. support τ− -tilting) subcategory of Mod-R . We also study the theory in Rep(Q,A) , where Q is a finite and acyclic quiver. In particular, we give an algorithm to construct support τ -tilting subcategories in Rep(Q,A) from certain support τ -tilting subcategories of A .
Fil: Asadollahi, Javad. University Of Isfahan; Irán
Fil: Sadeghi, Somayeh. University Of Isfahan; Irán
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
description The main theme of this paper is to study τ -tilting subcategories in an abelian category A with enough projective objects. We introduce the notion of τ -cotorsion torsion triples and investigate a bijection between the collection of τ -cotorsion torsion triples in A and the collection of support τ -tilting subcategories of A , generalizing the bijection by Bauer, Botnan, Oppermann, and Steen between the collection of cotorsion torsion triples and the collection of tilting subcategories of A . General definitions and results are exemplified using persistent modules. If A=Mod-R , where R is a unitary associative ring, we characterize all support τ -tilting (resp. all support τ− -tilting) subcategories of Mod-R in terms of finendo quasitilting (resp. quasicotilting) modules. As a result, it will be shown that every silting module (resp. every cosilting module) induces a support τ -tilting (resp. support τ− -tilting) subcategory of Mod-R . We also study the theory in Rep(Q,A) , where Q is a finite and acyclic quiver. In particular, we give an algorithm to construct support τ -tilting subcategories in Rep(Q,A) from certain support τ -tilting subcategories of A .
publishDate 2024
dc.date.none.fl_str_mv 2024-03
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/11336/235363
Asadollahi, Javad; Sadeghi, Somayeh; Treffinger Cienfuegos, Hipolito José; On tau-tilting subcategories; Canadian Mathematical Soc; Canadian Journal Of Mathematics; 3-2024; 1-38
0008-414X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/235363
identifier_str_mv Asadollahi, Javad; Sadeghi, Somayeh; Treffinger Cienfuegos, Hipolito José; On tau-tilting subcategories; Canadian Mathematical Soc; Canadian Journal Of Mathematics; 3-2024; 1-38
0008-414X
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/product/identifier/S0008414X24000221/type/journal_article
info:eu-repo/semantics/altIdentifier/doi/10.4153/S0008414X24000221
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2207.00457
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Canadian Mathematical Soc
publisher.none.fl_str_mv Canadian Mathematical Soc
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 13.070432

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