Comparison morphisms between two projective resolutions of monomial algebras

Autores
Redondo, Maria Julia; Roman, Lucrecia Juliana
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We construct comparison morphisms between two well-known projective resolutions of a monomial algebra A : the bar resolution Bar A and Bardzell’s resolution Ap A ; the first one is used to define the cup product and the Lie bracket on the Hochschild cohomology HH ∗ ( A ) and the second one has been shown to be an efficient tool for computation of these cohomology groups. The constructed comparison morphisms allow us to show that the cup product restricted to even degrees of the Hochschild cohomology has a very simple description. Moreover, for A = k Q/I a monomial algebra such that dim k e i Ae j = 1 whenever there exists an arrow α : i → j ∈ Q 1 , we describe the Lie action of the Lie algebra HH 1 ( A ) on HH ∗ ( A ).
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
Fil: Roman, Lucrecia Juliana. 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
ALGEBRA
COHOMOLOGY
MORPHISMS
COMPARISON
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:11336/64674
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Comparison morphisms between two projective resolutions of monomial algebrasRedondo, Maria JuliaRoman, Lucrecia JulianaALGEBRACOHOMOLOGYMORPHISMSCOMPARISONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We construct comparison morphisms between two well-known projective resolutions of a monomial algebra A : the bar resolution Bar A and Bardzell’s resolution Ap A ; the first one is used to define the cup product and the Lie bracket on the Hochschild cohomology HH ∗ ( A ) and the second one has been shown to be an efficient tool for computation of these cohomology groups. The constructed comparison morphisms allow us to show that the cup product restricted to even degrees of the Hochschild cohomology has a very simple description. Moreover, for A = k Q/I a monomial algebra such that dim k e i Ae j = 1 whenever there exists an arrow α : i → j ∈ Q 1 , we describe the Lie action of the Lie algebra HH 1 ( A ) on HH ∗ ( A ).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; ArgentinaFil: Roman, Lucrecia Juliana. 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; ArgentinaUnión Matemática Argentina2017-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/64674Redondo, Maria Julia; Roman, Lucrecia Juliana; Comparison morphisms between two projective resolutions of monomial algebras; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 59; 1; 7-2017; 1-310041-69321669-9637CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v59n1/v59n1a01.pdfinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1612.02308info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:35:38Zoai:ri.conicet.gov.ar:11336/64674instacron: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 09:35:38.302CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Comparison morphisms between two projective resolutions of monomial algebras
title Comparison morphisms between two projective resolutions of monomial algebras
spellingShingle Comparison morphisms between two projective resolutions of monomial algebras
Redondo, Maria Julia
ALGEBRA
COHOMOLOGY
MORPHISMS
COMPARISON
title_short Comparison morphisms between two projective resolutions of monomial algebras
title_full Comparison morphisms between two projective resolutions of monomial algebras
title_fullStr Comparison morphisms between two projective resolutions of monomial algebras
title_full_unstemmed Comparison morphisms between two projective resolutions of monomial algebras
title_sort Comparison morphisms between two projective resolutions of monomial algebras
dc.creator.none.fl_str_mv Redondo, Maria Julia
Roman, Lucrecia Juliana
author Redondo, Maria Julia
author_facet Redondo, Maria Julia
Roman, Lucrecia Juliana
author_role author
author2 Roman, Lucrecia Juliana
author2_role author
dc.subject.none.fl_str_mv ALGEBRA
COHOMOLOGY
MORPHISMS
COMPARISON
topic ALGEBRA
COHOMOLOGY
MORPHISMS
COMPARISON
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 construct comparison morphisms between two well-known projective resolutions of a monomial algebra A : the bar resolution Bar A and Bardzell’s resolution Ap A ; the first one is used to define the cup product and the Lie bracket on the Hochschild cohomology HH ∗ ( A ) and the second one has been shown to be an efficient tool for computation of these cohomology groups. The constructed comparison morphisms allow us to show that the cup product restricted to even degrees of the Hochschild cohomology has a very simple description. Moreover, for A = k Q/I a monomial algebra such that dim k e i Ae j = 1 whenever there exists an arrow α : i → j ∈ Q 1 , we describe the Lie action of the Lie algebra HH 1 ( A ) on HH ∗ ( A ).
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
Fil: Roman, Lucrecia Juliana. 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 We construct comparison morphisms between two well-known projective resolutions of a monomial algebra A : the bar resolution Bar A and Bardzell’s resolution Ap A ; the first one is used to define the cup product and the Lie bracket on the Hochschild cohomology HH ∗ ( A ) and the second one has been shown to be an efficient tool for computation of these cohomology groups. The constructed comparison morphisms allow us to show that the cup product restricted to even degrees of the Hochschild cohomology has a very simple description. Moreover, for A = k Q/I a monomial algebra such that dim k e i Ae j = 1 whenever there exists an arrow α : i → j ∈ Q 1 , we describe the Lie action of the Lie algebra HH 1 ( A ) on HH ∗ ( A ).
publishDate 2017
dc.date.none.fl_str_mv 2017-07
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/11336/64674
Redondo, Maria Julia; Roman, Lucrecia Juliana; Comparison morphisms between two projective resolutions of monomial algebras; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 59; 1; 7-2017; 1-31
0041-6932
1669-9637
CONICET Digital
CONICET
url http://hdl.handle.net/11336/64674
identifier_str_mv Redondo, Maria Julia; Roman, Lucrecia Juliana; Comparison morphisms between two projective resolutions of monomial algebras; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 59; 1; 7-2017; 1-31
0041-6932
1669-9637
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v59n1/v59n1a01.pdf
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1612.02308
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 Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
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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