On the multi-Koszul property for connected algebras
- Autores
- Herscovich Ramoneda, Estanislao Benito
- 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 locally finite dimensional nonnegatively graded connected algebra, 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. It also extends and generalizes the definition recently introduced by the author and A. Rey. In order to simplify the exposition we consider the minimal graded projective resolution of the algebra A as a bimodule, which may be used to compute the corresponding Hochschild (co)homology groups. This new definition includes several new interesting examples, e.g. the super Yang-Mills algebras introduced by M. Movshev and A. Schwarz, which are not generalized Koszul or even multi-Koszul for the previous definition given by the author and Rey. On the other hand, we provide an equivalent description of the new definition in terms of the Tor (or Ext) groups, and we show that several of the typical homological computations performed for the generalized Koszul algebras are also possible in this more general setting. In particular, we give an explicit description of the A_infinity-algebra structure of the Yoneda algebra of a multi-Koszul algebra. We also show that a finitely generated multi-Koszul algebra with a finite dimensional space of relations is a K_2 algebra in the sense of T. Cassidy and B. Shelton.
Fil: Herscovich Ramoneda, Estanislao Benito. Université Grenoble I; Francia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina - Materia
-
Koszul algebra
Yoneda algebra
Homological algebra
A_infinity algebras - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/14932
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On the multi-Koszul property for connected algebrasHerscovich Ramoneda, Estanislao BenitoKoszul algebraYoneda algebraHomological algebraA_infinity algebrashttps://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 locally finite dimensional nonnegatively graded connected algebra, 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. It also extends and generalizes the definition recently introduced by the author and A. Rey. In order to simplify the exposition we consider the minimal graded projective resolution of the algebra A as a bimodule, which may be used to compute the corresponding Hochschild (co)homology groups. This new definition includes several new interesting examples, e.g. the super Yang-Mills algebras introduced by M. Movshev and A. Schwarz, which are not generalized Koszul or even multi-Koszul for the previous definition given by the author and Rey. On the other hand, we provide an equivalent description of the new definition in terms of the Tor (or Ext) groups, and we show that several of the typical homological computations performed for the generalized Koszul algebras are also possible in this more general setting. In particular, we give an explicit description of the A_infinity-algebra structure of the Yoneda algebra of a multi-Koszul algebra. We also show that a finitely generated multi-Koszul algebra with a finite dimensional space of relations is a K_2 algebra in the sense of T. Cassidy and B. Shelton.Fil: Herscovich Ramoneda, Estanislao Benito. Université Grenoble I; Francia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaUniv Bielefeld2013-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14932Herscovich Ramoneda, Estanislao Benito; On the multi-Koszul property for connected algebras; Univ Bielefeld; Documenta Mathematica; 18; 12-2013; 1301-13471431-0643enginfo:eu-repo/semantics/altIdentifier/url/https://www.math.uni-bielefeld.de/documenta/vol-18/41.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:40:29Zoai:ri.conicet.gov.ar:11336/14932instacron: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 10:40:30.137CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
On the multi-Koszul property for connected algebras |
title |
On the multi-Koszul property for connected algebras |
spellingShingle |
On the multi-Koszul property for connected algebras Herscovich Ramoneda, Estanislao Benito Koszul algebra Yoneda algebra Homological algebra A_infinity algebras |
title_short |
On the multi-Koszul property for connected algebras |
title_full |
On the multi-Koszul property for connected algebras |
title_fullStr |
On the multi-Koszul property for connected algebras |
title_full_unstemmed |
On the multi-Koszul property for connected algebras |
title_sort |
On the multi-Koszul property for connected algebras |
dc.creator.none.fl_str_mv |
Herscovich Ramoneda, Estanislao Benito |
author |
Herscovich Ramoneda, Estanislao Benito |
author_facet |
Herscovich Ramoneda, Estanislao Benito |
author_role |
author |
dc.subject.none.fl_str_mv |
Koszul algebra Yoneda algebra Homological algebra A_infinity algebras |
topic |
Koszul algebra Yoneda algebra Homological algebra A_infinity 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 |
In this article we introduce the notion of multi-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, 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. It also extends and generalizes the definition recently introduced by the author and A. Rey. In order to simplify the exposition we consider the minimal graded projective resolution of the algebra A as a bimodule, which may be used to compute the corresponding Hochschild (co)homology groups. This new definition includes several new interesting examples, e.g. the super Yang-Mills algebras introduced by M. Movshev and A. Schwarz, which are not generalized Koszul or even multi-Koszul for the previous definition given by the author and Rey. On the other hand, we provide an equivalent description of the new definition in terms of the Tor (or Ext) groups, and we show that several of the typical homological computations performed for the generalized Koszul algebras are also possible in this more general setting. In particular, we give an explicit description of the A_infinity-algebra structure of the Yoneda algebra of a multi-Koszul algebra. We also show that a finitely generated multi-Koszul algebra with a finite dimensional space of relations is a K_2 algebra in the sense of T. Cassidy and B. Shelton. Fil: Herscovich Ramoneda, Estanislao Benito. Université Grenoble I; Francia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina |
description |
In this article we introduce the notion of multi-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, 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. It also extends and generalizes the definition recently introduced by the author and A. Rey. In order to simplify the exposition we consider the minimal graded projective resolution of the algebra A as a bimodule, which may be used to compute the corresponding Hochschild (co)homology groups. This new definition includes several new interesting examples, e.g. the super Yang-Mills algebras introduced by M. Movshev and A. Schwarz, which are not generalized Koszul or even multi-Koszul for the previous definition given by the author and Rey. On the other hand, we provide an equivalent description of the new definition in terms of the Tor (or Ext) groups, and we show that several of the typical homological computations performed for the generalized Koszul algebras are also possible in this more general setting. In particular, we give an explicit description of the A_infinity-algebra structure of the Yoneda algebra of a multi-Koszul algebra. We also show that a finitely generated multi-Koszul algebra with a finite dimensional space of relations is a K_2 algebra in the sense of T. Cassidy and B. Shelton. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-12 |
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/11336/14932 Herscovich Ramoneda, Estanislao Benito; On the multi-Koszul property for connected algebras; Univ Bielefeld; Documenta Mathematica; 18; 12-2013; 1301-1347 1431-0643 |
url |
http://hdl.handle.net/11336/14932 |
identifier_str_mv |
Herscovich Ramoneda, Estanislao Benito; On the multi-Koszul property for connected algebras; Univ Bielefeld; Documenta Mathematica; 18; 12-2013; 1301-1347 1431-0643 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.math.uni-bielefeld.de/documenta/vol-18/41.pdf |
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 |
Univ Bielefeld |
publisher.none.fl_str_mv |
Univ Bielefeld |
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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