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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14932

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spelling 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
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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