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dc.contributor.author
Berger, Roland  
dc.contributor.author
Lambre, Thierry  
dc.contributor.author
Solotar, Andrea Leonor  
dc.date.available
2019-01-31T18:46:00Z  
dc.date.issued
2018-05  
dc.identifier.citation
Berger, Roland; Lambre, Thierry; Solotar, Andrea Leonor; Koszul calculus; Cambridge University Press; Glasgow Mathematical Journal; 60; 2; 5-2018; 361-399  
dc.identifier.issn
0017-0895  
dc.identifier.uri
http://hdl.handle.net/11336/69131  
dc.description.abstract
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.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Cambridge University Press  
dc.relation
https://doi.org/10.1017/S0017089518000137  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
Koszul  
dc.subject
Quadratic Algebra  
dc.subject
Hochschild  
dc.subject
Cup Product  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Koszul calculus  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2019-01-23T17:19:06Z  
dc.journal.volume
60  
dc.journal.number
2  
dc.journal.pagination
361-399  
dc.journal.pais
Reino Unido  
dc.journal.ciudad
Cambridge  
dc.description.fil
Fil: Berger, Roland. Centre National de la Recherche Scientifique; Francia. Université Jean Monnet; Francia  
dc.description.fil
Fil: Lambre, Thierry. Universite Blaise Pascal; Francia. Centre National de la Recherche Scientifique; Francia  
dc.description.fil
Fil: 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"; Argentina  
dc.journal.title
Glasgow Mathematical Journal  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1017/S0017089517000167  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/koszul-calculus/3C88B4F8A1123BAC193B64F0631E49CC  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1512.00183  

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