Koszul calculus

We present a calculus that is well-adapted to homogeneous quadratic algebras. We define this calculus on Koszul cohomology - resp. homology - by cup products - resp. cap products. The Koszul homology and cohomology are interpreted in terms of derived categories. If the algebra is not Koszul, then Ko...

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Detalhes bibliográficos
Autores: Berger, Roland, Lambre, Thierry, Solotar, Andrea Leonor
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/69131
Acesso em linha:http://hdl.handle.net/11336/69131
Access Level:acceso abierto
Palavra-chave:Koszul
Quadratic algebra
Hochschild
Cup product
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Koszul calculusBerger, RolandLambre, ThierrySolotar, Andrea LeonorKoszulQuadratic algebraHochschildCup producthttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a calculus that is well-adapted to homogeneous quadratic algebras. We define this calculus on Koszul cohomology - resp. homology - by cup products - resp. cap products. The Koszul homology and cohomology are interpreted in terms of derived categories. If the algebra is not Koszul, then Koszul (co)homology provides different information than Hochschild (co)homology. As an application of our calculus, the Koszul duality for Koszul cohomology algebras is proved for any quadratic algebra, and this duality is extended in some sense to Koszul homology. So, the true nature of the Koszul duality theorem is independent of any assumption on the quadratic algebra. We compute explicitly this calculus on a non-Koszul example.Fil: Berger, Roland. Centre National de la Recherche Scientifique; Francia. Université Jean Monnet; FranciaFil: Lambre, Thierry. Universite Blaise Pascal; Francia. Centre National de la Recherche Scientifique; FranciaFil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaCambridge University Press2018-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/69131Berger, Roland; Lambre, Thierry; Solotar, Andrea Leonor; Koszul calculus; Cambridge University Press; Glasgow Mathematical Journal; 60; 2; 5-2018; 361-3990017-0895CONICET DigitalCONICETenghttps://doi.org/10.1017/S0017089518000137info:eu-repo/semantics/altIdentifier/doi/10.1017/S0017089517000167info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/koszul-calculus/3C88B4F8A1123BAC193B64F0631E49CCinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1512.00183info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:57:48Zoai:ri.conicet.gov.ar:11336/69131instacron: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:34982024-05-08 13:57:48.505CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Koszul calculus
title Koszul calculus
spellingShingle Koszul calculus
Berger, Roland
Koszul
Quadratic algebra
Hochschild
Cup product
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Koszul calculus
title_full Koszul calculus
title_fullStr Koszul calculus
title_full_unstemmed Koszul calculus
title_sort Koszul calculus
dc.creator.none.fl_str_mv Berger, Roland
Lambre, Thierry
Solotar, Andrea Leonor
author Berger, Roland
author_facet Berger, Roland
Lambre, Thierry
Solotar, Andrea Leonor
author_role author
author2 Lambre, Thierry
Solotar, Andrea Leonor
author2_role author
author
dc.subject.none.fl_str_mv Koszul
Quadratic algebra
Hochschild
Cup product
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Koszul
Quadratic algebra
Hochschild
Cup product
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description We present a calculus that is well-adapted to homogeneous quadratic algebras. We define this calculus on Koszul cohomology - resp. homology - by cup products - resp. cap products. The Koszul homology and cohomology are interpreted in terms of derived categories. If the algebra is not Koszul, then Koszul (co)homology provides different information than Hochschild (co)homology. As an application of our calculus, the Koszul duality for Koszul cohomology algebras is proved for any quadratic algebra, and this duality is extended in some sense to Koszul homology. So, the true nature of the Koszul duality theorem is independent of any assumption on the quadratic algebra. We compute explicitly this calculus on a non-Koszul example.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
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/11336/69131
Berger, Roland; Lambre, Thierry; Solotar, Andrea Leonor; Koszul calculus; Cambridge University Press; Glasgow Mathematical Journal; 60; 2; 5-2018; 361-399
0017-0895
CONICET Digital
CONICET
url http://hdl.handle.net/11336/69131
identifier_str_mv Berger, Roland; Lambre, Thierry; Solotar, Andrea Leonor; Koszul calculus; Cambridge University Press; Glasgow Mathematical Journal; 60; 2; 5-2018; 361-399
0017-0895
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://doi.org/10.1017/S0017089518000137
info:eu-repo/semantics/altIdentifier/doi/10.1017/S0017089517000167
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/koszul-calculus/3C88B4F8A1123BAC193B64F0631E49CC
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1512.00183
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
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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