Lie–Rinehart and Hochschild cohomology for algebras of differential operators

Let be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a U-bimodule M and whose second page involves the Lie–Rinehart cohomology of the alge...

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Detalhes bibliográficos
Autores: Kordon, Francisco, Lambre, Thierry
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2021
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/157638
Acesso em linha:http://hdl.handle.net/11336/157638
Access Level:Acceso aberto
Palavra-chave:HOCHSCHILD COHOMOLOGY
LIE-RINEHART ALGEBRAS
ALGEBRAS OF DIFFERENTIAL OPERATORS
HYPERPLANE ARRANGEMENTS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Lie–Rinehart and Hochschild cohomology for algebras of differential operatorsKordon, FranciscoLambre, ThierryHOCHSCHILD COHOMOLOGYLIE-RINEHART ALGEBRASALGEBRAS OF DIFFERENTIAL OPERATORSHYPERPLANE ARRANGEMENTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a U-bimodule M and whose second page involves the Lie–Rinehart cohomology of the algebra and the Hochschild cohomology of S with values on M. After giving a convenient description of the involved algebraic structures we use the spectral sequence to compute explicitly the Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of three lines.Fil: Kordon, Francisco. Universite Blaise Pascal. Laboratoire de Mathematiques; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Lambre, Thierry. Universite Blaise Pascal. Laboratoire de Mathematiques; Francia. Centre National de la Recherche Scientifique; FranciaElsevier Science2021-01info: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/11336/157638Kordon, Francisco; Lambre, Thierry; Lie–Rinehart and Hochschild cohomology for algebras of differential operators; Elsevier Science; Journal of Pure and Applied Algebra; 225; 1; 1-2021; 1-280022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022404920301560info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2020.106456info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2006.01218info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:08:17Zoai:ri.conicet.gov.ar:11336/157638instacron: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 14:08:17.542CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Lie–Rinehart and Hochschild cohomology for algebras of differential operators
title Lie–Rinehart and Hochschild cohomology for algebras of differential operators
spellingShingle Lie–Rinehart and Hochschild cohomology for algebras of differential operators
Kordon, Francisco
HOCHSCHILD COHOMOLOGY
LIE-RINEHART ALGEBRAS
ALGEBRAS OF DIFFERENTIAL OPERATORS
HYPERPLANE ARRANGEMENTS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Lie–Rinehart and Hochschild cohomology for algebras of differential operators
title_full Lie–Rinehart and Hochschild cohomology for algebras of differential operators
title_fullStr Lie–Rinehart and Hochschild cohomology for algebras of differential operators
title_full_unstemmed Lie–Rinehart and Hochschild cohomology for algebras of differential operators
title_sort Lie–Rinehart and Hochschild cohomology for algebras of differential operators
dc.creator.none.fl_str_mv Kordon, Francisco
Lambre, Thierry
author Kordon, Francisco
author_facet Kordon, Francisco
Lambre, Thierry
author_role author
author2 Lambre, Thierry
author2_role author
dc.subject.none.fl_str_mv HOCHSCHILD COHOMOLOGY
LIE-RINEHART ALGEBRAS
ALGEBRAS OF DIFFERENTIAL OPERATORS
HYPERPLANE ARRANGEMENTS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic HOCHSCHILD COHOMOLOGY
LIE-RINEHART ALGEBRAS
ALGEBRAS OF DIFFERENTIAL OPERATORS
HYPERPLANE ARRANGEMENTS
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Let be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a U-bimodule M and whose second page involves the Lie–Rinehart cohomology of the algebra and the Hochschild cohomology of S with values on M. After giving a convenient description of the involved algebraic structures we use the spectral sequence to compute explicitly the Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of three lines.
publishDate 2021
dc.date.none.fl_str_mv 2021-01
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/11336/157638
Kordon, Francisco; Lambre, Thierry; Lie–Rinehart and Hochschild cohomology for algebras of differential operators; Elsevier Science; Journal of Pure and Applied Algebra; 225; 1; 1-2021; 1-28
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/157638
identifier_str_mv Kordon, Francisco; Lambre, Thierry; Lie–Rinehart and Hochschild cohomology for algebras of differential operators; Elsevier Science; Journal of Pure and Applied Algebra; 225; 1; 1-2021; 1-28
0022-4049
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022404920301560
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2020.106456
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2006.01218
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 15,812429

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