On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra

Autores
Assem, Ibrahim; Redondo, Maria Julia; Schiffler, Ralf
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a cluster-tilted algebra B, we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation-extension of C, then we show that if B is tame, then HH1(B) is isomorphic, as a kvector space, to the direct sum of HH1(C) with knB,C , where nB,C is an invariant linking the bound quivers of B and C. In the representation-finite case, HH1(B) can be read off simply by looking at the quiver of B.
Fil: Assem, Ibrahim. University Of Sherbrooke; Canadá
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Schiffler, Ralf. University Of Sherbrooke; Canadá
Materia
Cluster-Tilded Algebra
Hochschild Cohomology
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:11336/11872
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the First Hochschild Cohomology Group of a Cluster-Tilted AlgebraAssem, IbrahimRedondo, Maria JuliaSchiffler, RalfCluster-Tilded AlgebraHochschild Cohomologyhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a cluster-tilted algebra B, we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation-extension of C, then we show that if B is tame, then HH1(B) is isomorphic, as a kvector space, to the direct sum of HH1(C) with knB,C , where nB,C is an invariant linking the bound quivers of B and C. In the representation-finite case, HH1(B) can be read off simply by looking at the quiver of B.Fil: Assem, Ibrahim. University Of Sherbrooke; CanadáFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Schiffler, Ralf. University Of Sherbrooke; CanadáSpringer2015-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/11872Assem, Ibrahim; Redondo, Maria Julia; Schiffler, Ralf; On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra; Springer; Algebras And Representation Theory; 18; 6; 12-2015; 1547-15761386-923Xenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10468-015-9551-xinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10468-015-9551-xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:01:04Zoai:ri.conicet.gov.ar:11336/11872instacron: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:34982025-11-05 10:01:04.607CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
title On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
spellingShingle On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
Assem, Ibrahim
Cluster-Tilded Algebra
Hochschild Cohomology
title_short On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
title_full On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
title_fullStr On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
title_full_unstemmed On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
title_sort On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
dc.creator.none.fl_str_mv Assem, Ibrahim
Redondo, Maria Julia
Schiffler, Ralf
author Assem, Ibrahim
author_facet Assem, Ibrahim
Redondo, Maria Julia
Schiffler, Ralf
author_role author
author2 Redondo, Maria Julia
Schiffler, Ralf
author2_role author
author
dc.subject.none.fl_str_mv Cluster-Tilded Algebra
Hochschild Cohomology
topic Cluster-Tilded Algebra
Hochschild Cohomology
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a cluster-tilted algebra B, we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation-extension of C, then we show that if B is tame, then HH1(B) is isomorphic, as a kvector space, to the direct sum of HH1(C) with knB,C , where nB,C is an invariant linking the bound quivers of B and C. In the representation-finite case, HH1(B) can be read off simply by looking at the quiver of B.
Fil: Assem, Ibrahim. University Of Sherbrooke; Canadá
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Schiffler, Ralf. University Of Sherbrooke; Canadá
description Given a cluster-tilted algebra B, we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra such that B is the relation-extension of C, then we show that if B is tame, then HH1(B) is isomorphic, as a kvector space, to the direct sum of HH1(C) with knB,C , where nB,C is an invariant linking the bound quivers of B and C. In the representation-finite case, HH1(B) can be read off simply by looking at the quiver of B.
publishDate 2015
dc.date.none.fl_str_mv 2015-12
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/11336/11872
Assem, Ibrahim; Redondo, Maria Julia; Schiffler, Ralf; On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra; Springer; Algebras And Representation Theory; 18; 6; 12-2015; 1547-1576
1386-923X
url http://hdl.handle.net/11336/11872
identifier_str_mv Assem, Ibrahim; Redondo, Maria Julia; Schiffler, Ralf; On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra; Springer; Algebras And Representation Theory; 18; 6; 12-2015; 1547-1576
1386-923X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10468-015-9551-x
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10468-015-9551-x
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 Springer
publisher.none.fl_str_mv Springer
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 13.087074

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