On a definition of multi-Koszul algebras
- Autores
- Herscovich Ramoneda, Estanislao Benito; Rey, Andrea
- Año de publicación
- 2013
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this article we introduce the notion of multi-Koszul algebra for the case of a nonnegatively graded connected algebra with a finite number of generators of degree 1 and with a finite number of relations, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous algebras, which were in turn an extension of Koszul algebras introduced by S. Priddy. Our definition is in some sense as closest as possible to the one given in the homogeneous case. Indeed, we give an equivalent description of the new definition in terms of the Tor (or Ext) groups, similar to the existing one for homogeneous algebras, and also a complete characterization of the multi-Koszul property, which derives from the study of some associated homogeneous algebras, providing a very strong link between the new definition and the generalized Koszul property for the associated homogeneous algebras mentioned before. We further obtain an explicit description of the Yoneda algebra of a multi-Koszul algebra. As a consequence, we get that the Yoneda algebra of a multi-Koszul algebra is generated in degrees 1 and 2, so a K2 algebra in the sense of T. Cassidy and B. Shelton. We also exhibit several examples and we provide a minimal graded projective resolution of the algebra A considered as an A-bimodule, which may be used to compute the Hochschild (co)homology groups. Finally, we find necessary and sufficient conditions on some (fixed) sequences of vector subspaces of the tensor powers of the base space V to obtain in this case the multi-Koszul property in the case we have relations in only two degrees.
Fil: Herscovich Ramoneda, Estanislao Benito. Universite Joseph Fourier; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rey, Andrea. Universidad de San Andrés; Argentina - Materia
-
Homological Algebra
Koszul Algebras
Yoneda Algebra - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/83269
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On a definition of multi-Koszul algebrasHerscovich Ramoneda, Estanislao BenitoRey, AndreaHomological AlgebraKoszul AlgebrasYoneda Algebrahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article we introduce the notion of multi-Koszul algebra for the case of a nonnegatively graded connected algebra with a finite number of generators of degree 1 and with a finite number of relations, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous algebras, which were in turn an extension of Koszul algebras introduced by S. Priddy. Our definition is in some sense as closest as possible to the one given in the homogeneous case. Indeed, we give an equivalent description of the new definition in terms of the Tor (or Ext) groups, similar to the existing one for homogeneous algebras, and also a complete characterization of the multi-Koszul property, which derives from the study of some associated homogeneous algebras, providing a very strong link between the new definition and the generalized Koszul property for the associated homogeneous algebras mentioned before. We further obtain an explicit description of the Yoneda algebra of a multi-Koszul algebra. As a consequence, we get that the Yoneda algebra of a multi-Koszul algebra is generated in degrees 1 and 2, so a K2 algebra in the sense of T. Cassidy and B. Shelton. We also exhibit several examples and we provide a minimal graded projective resolution of the algebra A considered as an A-bimodule, which may be used to compute the Hochschild (co)homology groups. Finally, we find necessary and sufficient conditions on some (fixed) sequences of vector subspaces of the tensor powers of the base space V to obtain in this case the multi-Koszul property in the case we have relations in only two degrees.Fil: Herscovich Ramoneda, Estanislao Benito. Universite Joseph Fourier; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rey, Andrea. Universidad de San Andrés; ArgentinaAcademic Press Inc Elsevier Science2013-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/83269Herscovich Ramoneda, Estanislao Benito; Rey, Andrea; On a definition of multi-Koszul algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 376; 2-2013; 196-2270021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2012.11.030info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869312005959info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:01:02Zoai:ri.conicet.gov.ar:11336/83269instacron: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 10:01:02.751CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
On a definition of multi-Koszul algebras |
title |
On a definition of multi-Koszul algebras |
spellingShingle |
On a definition of multi-Koszul algebras Herscovich Ramoneda, Estanislao Benito Homological Algebra Koszul Algebras Yoneda Algebra |
title_short |
On a definition of multi-Koszul algebras |
title_full |
On a definition of multi-Koszul algebras |
title_fullStr |
On a definition of multi-Koszul algebras |
title_full_unstemmed |
On a definition of multi-Koszul algebras |
title_sort |
On a definition of multi-Koszul algebras |
dc.creator.none.fl_str_mv |
Herscovich Ramoneda, Estanislao Benito Rey, Andrea |
author |
Herscovich Ramoneda, Estanislao Benito |
author_facet |
Herscovich Ramoneda, Estanislao Benito Rey, Andrea |
author_role |
author |
author2 |
Rey, Andrea |
author2_role |
author |
dc.subject.none.fl_str_mv |
Homological Algebra Koszul Algebras Yoneda Algebra |
topic |
Homological Algebra Koszul Algebras Yoneda Algebra |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In this article we introduce the notion of multi-Koszul algebra for the case of a nonnegatively graded connected algebra with a finite number of generators of degree 1 and with a finite number of relations, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous algebras, which were in turn an extension of Koszul algebras introduced by S. Priddy. Our definition is in some sense as closest as possible to the one given in the homogeneous case. Indeed, we give an equivalent description of the new definition in terms of the Tor (or Ext) groups, similar to the existing one for homogeneous algebras, and also a complete characterization of the multi-Koszul property, which derives from the study of some associated homogeneous algebras, providing a very strong link between the new definition and the generalized Koszul property for the associated homogeneous algebras mentioned before. We further obtain an explicit description of the Yoneda algebra of a multi-Koszul algebra. As a consequence, we get that the Yoneda algebra of a multi-Koszul algebra is generated in degrees 1 and 2, so a K2 algebra in the sense of T. Cassidy and B. Shelton. We also exhibit several examples and we provide a minimal graded projective resolution of the algebra A considered as an A-bimodule, which may be used to compute the Hochschild (co)homology groups. Finally, we find necessary and sufficient conditions on some (fixed) sequences of vector subspaces of the tensor powers of the base space V to obtain in this case the multi-Koszul property in the case we have relations in only two degrees. Fil: Herscovich Ramoneda, Estanislao Benito. Universite Joseph Fourier; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Rey, Andrea. Universidad de San Andrés; Argentina |
description |
In this article we introduce the notion of multi-Koszul algebra for the case of a nonnegatively graded connected algebra with a finite number of generators of degree 1 and with a finite number of relations, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous algebras, which were in turn an extension of Koszul algebras introduced by S. Priddy. Our definition is in some sense as closest as possible to the one given in the homogeneous case. Indeed, we give an equivalent description of the new definition in terms of the Tor (or Ext) groups, similar to the existing one for homogeneous algebras, and also a complete characterization of the multi-Koszul property, which derives from the study of some associated homogeneous algebras, providing a very strong link between the new definition and the generalized Koszul property for the associated homogeneous algebras mentioned before. We further obtain an explicit description of the Yoneda algebra of a multi-Koszul algebra. As a consequence, we get that the Yoneda algebra of a multi-Koszul algebra is generated in degrees 1 and 2, so a K2 algebra in the sense of T. Cassidy and B. Shelton. We also exhibit several examples and we provide a minimal graded projective resolution of the algebra A considered as an A-bimodule, which may be used to compute the Hochschild (co)homology groups. Finally, we find necessary and sufficient conditions on some (fixed) sequences of vector subspaces of the tensor powers of the base space V to obtain in this case the multi-Koszul property in the case we have relations in only two degrees. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-02 |
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/11336/83269 Herscovich Ramoneda, Estanislao Benito; Rey, Andrea; On a definition of multi-Koszul algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 376; 2-2013; 196-227 0021-8693 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/83269 |
identifier_str_mv |
Herscovich Ramoneda, Estanislao Benito; Rey, Andrea; On a definition of multi-Koszul algebras; Academic Press Inc Elsevier Science; Journal of Algebra; 376; 2-2013; 196-227 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.2012.11.030 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869312005959 |
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 |
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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.070432 |