Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ
- Autores
- Mendoza Hernández, Octavio; Platzeck, Maria Ines
- Año de publicación
- 2003
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let Δ be a Dynkin diagram and k an algebraically closed field. Let A be an iterated tilted finite-dimensional k-algebra of type Δ and denote by  its repetitive algebra. We approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the Auslander-Reiten quiver ΓA of A in the Auslander-Reiten quiver Γ(mod(Â)) ≃ ℤΔ of the stable category mod(Â). Let T be a trivial extension of finite representation type and Cartan class Δ. Assume that we know the vertices of ℤΔ corresponding to the radicals of the indecomposable projective T-modules. We determine the embedding of ΓA in ℤΔ for any algebra A such that T(A) ≃ T.
Fil: Mendoza Hernández, Octavio. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Platzeck, Maria Ines. 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
-
Modules
Artin algebras - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/95361
Ver los metadatos del registro completo
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Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔMendoza Hernández, OctavioPlatzeck, Maria InesModulesArtin algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let Δ be a Dynkin diagram and k an algebraically closed field. Let A be an iterated tilted finite-dimensional k-algebra of type Δ and denote by  its repetitive algebra. We approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the Auslander-Reiten quiver ΓA of A in the Auslander-Reiten quiver Γ(mod(Â)) ≃ ℤΔ of the stable category mod(Â). Let T be a trivial extension of finite representation type and Cartan class Δ. Assume that we know the vertices of ℤΔ corresponding to the radicals of the indecomposable projective T-modules. We determine the embedding of ΓA in ℤΔ for any algebra A such that T(A) ≃ T.Fil: Mendoza Hernández, Octavio. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Platzeck, Maria Ines. 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 Science2003-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/95361Mendoza Hernández, Octavio; Platzeck, Maria Ines; Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ; Academic Press Inc Elsevier Science; Journal of Algebra; 265; 1; 7-2003; 247-2630021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/S0021-8693%2803%2900161-3info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869303001613info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:52:02Zoai:ri.conicet.gov.ar:11336/95361instacron: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 09:52:03.154CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ |
| title |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ |
| spellingShingle |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ Mendoza Hernández, Octavio Modules Artin algebras |
| title_short |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ |
| title_full |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ |
| title_fullStr |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ |
| title_full_unstemmed |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ |
| title_sort |
Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ |
| dc.creator.none.fl_str_mv |
Mendoza Hernández, Octavio Platzeck, Maria Ines |
| author |
Mendoza Hernández, Octavio |
| author_facet |
Mendoza Hernández, Octavio Platzeck, Maria Ines |
| author_role |
author |
| author2 |
Platzeck, Maria Ines |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Modules Artin algebras |
| topic |
Modules Artin algebras |
| 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 Δ be a Dynkin diagram and k an algebraically closed field. Let A be an iterated tilted finite-dimensional k-algebra of type Δ and denote by  its repetitive algebra. We approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the Auslander-Reiten quiver ΓA of A in the Auslander-Reiten quiver Γ(mod(Â)) ≃ ℤΔ of the stable category mod(Â). Let T be a trivial extension of finite representation type and Cartan class Δ. Assume that we know the vertices of ℤΔ corresponding to the radicals of the indecomposable projective T-modules. We determine the embedding of ΓA in ℤΔ for any algebra A such that T(A) ≃ T. Fil: Mendoza Hernández, Octavio. Universidad Nacional del Sur. Departamento de Matemática; Argentina Fil: Platzeck, Maria Ines. 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 |
Let Δ be a Dynkin diagram and k an algebraically closed field. Let A be an iterated tilted finite-dimensional k-algebra of type Δ and denote by  its repetitive algebra. We approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the Auslander-Reiten quiver ΓA of A in the Auslander-Reiten quiver Γ(mod(Â)) ≃ ℤΔ of the stable category mod(Â). Let T be a trivial extension of finite representation type and Cartan class Δ. Assume that we know the vertices of ℤΔ corresponding to the radicals of the indecomposable projective T-modules. We determine the embedding of ΓA in ℤΔ for any algebra A such that T(A) ≃ T. |
| publishDate |
2003 |
| dc.date.none.fl_str_mv |
2003-07 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/95361 Mendoza Hernández, Octavio; Platzeck, Maria Ines; Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ; Academic Press Inc Elsevier Science; Journal of Algebra; 265; 1; 7-2003; 247-263 0021-8693 CONICET Digital CONICET |
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http://hdl.handle.net/11336/95361 |
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Mendoza Hernández, Octavio; Platzeck, Maria Ines; Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ; Academic Press Inc Elsevier Science; Journal of Algebra; 265; 1; 7-2003; 247-263 0021-8693 CONICET Digital CONICET |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/doi/10.1016/S0021-8693%2803%2900161-3 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869303001613 |
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Academic Press Inc Elsevier Science |
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Academic Press Inc Elsevier Science |
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