Covering functors without groups

Autores
De la Peña Mena, José Antonio; Redondo, Maria Julia
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation-finite algebra in [Ch. Riedtmann, Algebren, Darstellungsköcher, Überlagerungen und zurüch, Comment. Math. Helv. 55 (1980) 199-224] and later for finite-dimensional algebras in [K. Bongartz, P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (3) (1982) 331-378; P. Gabriel, The universal cover of a representation-finite algebra, in: Proc. Representation Theory I, Puebla, 1980, in: Lecture Notes in Math., vol. 903, Springer, 1981, pp. 68-105; R. Martínez-Villa, J.A. de la Peña, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (3) (1983) 277-292]. The best understood class of covering functors is that of Galois covering functorsF : A → B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Galois class and for which classical Galois covering-type results still hold. For instance, if F : A → B is a balanced covering functor, where A and B are linear categories over an algebraically closed field, and B is tame, then A is tame.
Fil: De la Peña Mena, José Antonio. Universidad Nacional Autónoma de México; México
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Materia
COVERINGS
REPRESENTATION
ALGEBRAS
GROUPS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/79550
Acceder
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spelling Covering functors without groupsDe la Peña Mena, José AntonioRedondo, Maria JuliaCOVERINGSREPRESENTATIONALGEBRASGROUPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation-finite algebra in [Ch. Riedtmann, Algebren, Darstellungsköcher, Überlagerungen und zurüch, Comment. Math. Helv. 55 (1980) 199-224] and later for finite-dimensional algebras in [K. Bongartz, P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (3) (1982) 331-378; P. Gabriel, The universal cover of a representation-finite algebra, in: Proc. Representation Theory I, Puebla, 1980, in: Lecture Notes in Math., vol. 903, Springer, 1981, pp. 68-105; R. Martínez-Villa, J.A. de la Peña, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (3) (1983) 277-292]. The best understood class of covering functors is that of Galois covering functorsF : A → B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Galois class and for which classical Galois covering-type results still hold. For instance, if F : A → B is a balanced covering functor, where A and B are linear categories over an algebraically closed field, and B is tame, then A is tame.Fil: De la Peña Mena, José Antonio. Universidad Nacional Autónoma de México; MéxicoFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaAcademic Press Inc Elsevier Science2009-06info: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/11336/79550De la Peña Mena, José Antonio; Redondo, Maria Julia; Covering functors without groups; Academic Press Inc Elsevier Science; Journal of Algebra; 321; 12; 6-2009; 3816-38260021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869309001483info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2009.02.023info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0803.4442info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:12:08Zoai:ri.conicet.gov.ar:11336/79550instacron: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:34982025-10-22 11:12:08.945CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Covering functors without groups
title Covering functors without groups
spellingShingle Covering functors without groups
De la Peña Mena, José Antonio
COVERINGS
REPRESENTATION
ALGEBRAS
GROUPS
title_short Covering functors without groups
title_full Covering functors without groups
title_fullStr Covering functors without groups
title_full_unstemmed Covering functors without groups
title_sort Covering functors without groups
dc.creator.none.fl_str_mv De la Peña Mena, José Antonio
Redondo, Maria Julia
author De la Peña Mena, José Antonio
author_facet De la Peña Mena, José Antonio
Redondo, Maria Julia
author_role author
author2 Redondo, Maria Julia
author2_role author
dc.subject.none.fl_str_mv COVERINGS
REPRESENTATION
ALGEBRAS
GROUPS
topic COVERINGS
REPRESENTATION
ALGEBRAS
GROUPS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation-finite algebra in [Ch. Riedtmann, Algebren, Darstellungsköcher, Überlagerungen und zurüch, Comment. Math. Helv. 55 (1980) 199-224] and later for finite-dimensional algebras in [K. Bongartz, P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (3) (1982) 331-378; P. Gabriel, The universal cover of a representation-finite algebra, in: Proc. Representation Theory I, Puebla, 1980, in: Lecture Notes in Math., vol. 903, Springer, 1981, pp. 68-105; R. Martínez-Villa, J.A. de la Peña, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (3) (1983) 277-292]. The best understood class of covering functors is that of Galois covering functorsF : A → B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Galois class and for which classical Galois covering-type results still hold. For instance, if F : A → B is a balanced covering functor, where A and B are linear categories over an algebraically closed field, and B is tame, then A is tame.
Fil: De la Peña Mena, José Antonio. Universidad Nacional Autónoma de México; México
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation-finite algebra in [Ch. Riedtmann, Algebren, Darstellungsköcher, Überlagerungen und zurüch, Comment. Math. Helv. 55 (1980) 199-224] and later for finite-dimensional algebras in [K. Bongartz, P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (3) (1982) 331-378; P. Gabriel, The universal cover of a representation-finite algebra, in: Proc. Representation Theory I, Puebla, 1980, in: Lecture Notes in Math., vol. 903, Springer, 1981, pp. 68-105; R. Martínez-Villa, J.A. de la Peña, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (3) (1983) 277-292]. The best understood class of covering functors is that of Galois covering functorsF : A → B determined by the action of a group of automorphisms of A. In this work we introduce the balanced covering functors which include the Galois class and for which classical Galois covering-type results still hold. For instance, if F : A → B is a balanced covering functor, where A and B are linear categories over an algebraically closed field, and B is tame, then A is tame.
publishDate 2009
dc.date.none.fl_str_mv 2009-06
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/11336/79550
De la Peña Mena, José Antonio; Redondo, Maria Julia; Covering functors without groups; Academic Press Inc Elsevier Science; Journal of Algebra; 321; 12; 6-2009; 3816-3826
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/79550
identifier_str_mv De la Peña Mena, José Antonio; Redondo, Maria Julia; Covering functors without groups; Academic Press Inc Elsevier Science; Journal of Algebra; 321; 12; 6-2009; 3816-3826
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/url/https://www.sciencedirect.com/science/article/pii/S0021869309001483
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2009.02.023
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0803.4442
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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 12.982451

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