Lie–Rinehart and Hochschild cohomology for algebras of differential operators
- Autores
- Kordon, Francisco; Lambre, Thierry
- Año de publicación
- 2021
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Fil: Kordon, Francisco. Universite Blaise Pascal. Laboratoire de Mathematiques; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Lambre, Thierry. Universite Blaise Pascal. Laboratoire de Mathematiques; Francia. Centre National de la Recherche Scientifique; Francia - Materia
-
HOCHSCHILD COHOMOLOGY
LIE-RINEHART ALGEBRAS
ALGEBRAS OF DIFFERENTIAL OPERATORS
HYPERPLANE ARRANGEMENTS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/157638
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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 Técnicas2025-09-29T10:19:48Zoai: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:34982025-09-29 10:19:49.298CONICET 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 |
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 |
topic |
HOCHSCHILD COHOMOLOGY LIE-RINEHART ALGEBRAS ALGEBRAS OF DIFFERENTIAL OPERATORS HYPERPLANE ARRANGEMENTS |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
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. Fil: Kordon, Francisco. Universite Blaise Pascal. Laboratoire de Mathematiques; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina Fil: Lambre, Thierry. Universite Blaise Pascal. Laboratoire de Mathematiques; Francia. Centre National de la Recherche Scientifique; Francia |
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 |
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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1844614172941221888 |
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13.070432 |