On syzygies over 2-Calabi–Yau tilted algebras

Autores
Garcia Elsener, Ana Clara; Schiffler, Ralf
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We characterize the syzygies and co-syzygies over 2-Calabi–Yau tilted algebras in terms of the Auslander–Reiten translation and the syzygy functor. We explore connections between the category of syzygies, the category of Cohen–Macaulay modules, the representation dimension of algebras and the Igusa–Todorov functions. In particular, we prove that the Igusa–Todorov dimensions of d-Gorenstein algebras are equal to d. For cluster-tilted algebras of Dynkin type D, we give a geometric description of the stable Cohen–Macaulay category in terms of tagged arcs in the punctured disc. We also describe the action of the syzygy functor in a geometric way. This description allows us to compute the Auslander–Reiten quiver of the stable Cohen–Macaulay category using tagged arcs and geometric moves.
Fil: Garcia Elsener, Ana Clara. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Schiffler, Ralf. University of Connecticut; Estados Unidos
Materia
2-CALABI–YAU TILTED ALGEBRA
CLUSTER-TILTED ALGEBRA
COHEN–MACAULAY MODULE
IGUSA–TODOROV FUNCTION
PUNCTURED POLYGON
SYZYGY
TRIANGULATED SURFACE
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:11336/178786
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/178786
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On syzygies over 2-Calabi–Yau tilted algebrasGarcia Elsener, Ana ClaraSchiffler, Ralf2-CALABI–YAU TILTED ALGEBRACLUSTER-TILTED ALGEBRACOHEN–MACAULAY MODULEIGUSA–TODOROV FUNCTIONPUNCTURED POLYGONSYZYGYTRIANGULATED SURFACEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We characterize the syzygies and co-syzygies over 2-Calabi–Yau tilted algebras in terms of the Auslander–Reiten translation and the syzygy functor. We explore connections between the category of syzygies, the category of Cohen–Macaulay modules, the representation dimension of algebras and the Igusa–Todorov functions. In particular, we prove that the Igusa–Todorov dimensions of d-Gorenstein algebras are equal to d. For cluster-tilted algebras of Dynkin type D, we give a geometric description of the stable Cohen–Macaulay category in terms of tagged arcs in the punctured disc. We also describe the action of the syzygy functor in a geometric way. This description allows us to compute the Auslander–Reiten quiver of the stable Cohen–Macaulay category using tagged arcs and geometric moves.Fil: Garcia Elsener, Ana Clara. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Schiffler, Ralf. University of Connecticut; Estados UnidosAcademic Press Inc Elsevier Science2017-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/178786Garcia Elsener, Ana Clara; Schiffler, Ralf; On syzygies over 2-Calabi–Yau tilted algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 470; 1-2017; 91-1210021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2016.08.035info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:30:54Zoai:ri.conicet.gov.ar:11336/178786instacron: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:34982025-09-17 11:30:55.192CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On syzygies over 2-Calabi–Yau tilted algebras
title On syzygies over 2-Calabi–Yau tilted algebras
spellingShingle On syzygies over 2-Calabi–Yau tilted algebras
Garcia Elsener, Ana Clara
2-CALABI–YAU TILTED ALGEBRA
CLUSTER-TILTED ALGEBRA
COHEN–MACAULAY MODULE
IGUSA–TODOROV FUNCTION
PUNCTURED POLYGON
SYZYGY
TRIANGULATED SURFACE
title_short On syzygies over 2-Calabi–Yau tilted algebras
title_full On syzygies over 2-Calabi–Yau tilted algebras
title_fullStr On syzygies over 2-Calabi–Yau tilted algebras
title_full_unstemmed On syzygies over 2-Calabi–Yau tilted algebras
title_sort On syzygies over 2-Calabi–Yau tilted algebras
dc.creator.none.fl_str_mv Garcia Elsener, Ana Clara
Schiffler, Ralf
author Garcia Elsener, Ana Clara
author_facet Garcia Elsener, Ana Clara
Schiffler, Ralf
author_role author
author2 Schiffler, Ralf
author2_role author
dc.subject.none.fl_str_mv 2-CALABI–YAU TILTED ALGEBRA
CLUSTER-TILTED ALGEBRA
COHEN–MACAULAY MODULE
IGUSA–TODOROV FUNCTION
PUNCTURED POLYGON
SYZYGY
TRIANGULATED SURFACE
topic 2-CALABI–YAU TILTED ALGEBRA
CLUSTER-TILTED ALGEBRA
COHEN–MACAULAY MODULE
IGUSA–TODOROV FUNCTION
PUNCTURED POLYGON
SYZYGY
TRIANGULATED SURFACE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We characterize the syzygies and co-syzygies over 2-Calabi–Yau tilted algebras in terms of the Auslander–Reiten translation and the syzygy functor. We explore connections between the category of syzygies, the category of Cohen–Macaulay modules, the representation dimension of algebras and the Igusa–Todorov functions. In particular, we prove that the Igusa–Todorov dimensions of d-Gorenstein algebras are equal to d. For cluster-tilted algebras of Dynkin type D, we give a geometric description of the stable Cohen–Macaulay category in terms of tagged arcs in the punctured disc. We also describe the action of the syzygy functor in a geometric way. This description allows us to compute the Auslander–Reiten quiver of the stable Cohen–Macaulay category using tagged arcs and geometric moves.
Fil: Garcia Elsener, Ana Clara. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina
Fil: Schiffler, Ralf. University of Connecticut; Estados Unidos
description We characterize the syzygies and co-syzygies over 2-Calabi–Yau tilted algebras in terms of the Auslander–Reiten translation and the syzygy functor. We explore connections between the category of syzygies, the category of Cohen–Macaulay modules, the representation dimension of algebras and the Igusa–Todorov functions. In particular, we prove that the Igusa–Todorov dimensions of d-Gorenstein algebras are equal to d. For cluster-tilted algebras of Dynkin type D, we give a geometric description of the stable Cohen–Macaulay category in terms of tagged arcs in the punctured disc. We also describe the action of the syzygy functor in a geometric way. This description allows us to compute the Auslander–Reiten quiver of the stable Cohen–Macaulay category using tagged arcs and geometric moves.
publishDate 2017
dc.date.none.fl_str_mv 2017-01
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/11336/178786
Garcia Elsener, Ana Clara; Schiffler, Ralf; On syzygies over 2-Calabi–Yau tilted algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 470; 1-2017; 91-121
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/178786
identifier_str_mv Garcia Elsener, Ana Clara; Schiffler, Ralf; On syzygies over 2-Calabi–Yau tilted algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 470; 1-2017; 91-121
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2016.08.035
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
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.001348

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