Hochschild (Co)Homology of Differential Operator Rings

Autores
Guccione, Jorge Alberto; Guccione, Juan Jose
Año de publicación
2001
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that the Hochschild homology of a differential operator kalgebra E = A#f U(g), is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗A^-∗, b∗). Moreover, when A is smooth and k is a characteristic zero field, we obtain a type of Hochschild-Kostant-Rosenberg theorem for these algebras. When A = k our complex reduce to the one obtained in [K] for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology.
Fil: Guccione, Jorge Alberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Guccione, Juan Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
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:11336/110409
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Hochschild (Co)Homology of Differential Operator RingsGuccione, Jorge AlbertoGuccione, Juan Josehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that the Hochschild homology of a differential operator kalgebra E = A#f U(g), is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗A^-∗, b∗). Moreover, when A is smooth and k is a characteristic zero field, we obtain a type of Hochschild-Kostant-Rosenberg theorem for these algebras. When A = k our complex reduce to the one obtained in [K] for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology.Fil: Guccione, Jorge Alberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Guccione, Juan Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAcademic Press Inc Elsevier Science2001-09info: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/11336/110409Guccione, Jorge Alberto; Guccione, Juan Jose; Hochschild (Co)Homology of Differential Operator Rings; Academic Press Inc Elsevier Science; Journal of Algebra; 243; 2; 9-2001; 596-6140021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021869301988672info:eu-repo/semantics/altIdentifier/doi/10.1006/jabr.2001.8867info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:00:56Zoai:ri.conicet.gov.ar:11336/110409instacron: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:34982025-10-22 11:00:56.847CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hochschild (Co)Homology of Differential Operator Rings
title Hochschild (Co)Homology of Differential Operator Rings
spellingShingle Hochschild (Co)Homology of Differential Operator Rings
Guccione, Jorge Alberto
title_short Hochschild (Co)Homology of Differential Operator Rings
title_full Hochschild (Co)Homology of Differential Operator Rings
title_fullStr Hochschild (Co)Homology of Differential Operator Rings
title_full_unstemmed Hochschild (Co)Homology of Differential Operator Rings
title_sort Hochschild (Co)Homology of Differential Operator Rings
dc.creator.none.fl_str_mv Guccione, Jorge Alberto
Guccione, Juan Jose
author Guccione, Jorge Alberto
author_facet Guccione, Jorge Alberto
Guccione, Juan Jose
author_role author
author2 Guccione, Juan Jose
author2_role author
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that the Hochschild homology of a differential operator kalgebra E = A#f U(g), is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗A^-∗, b∗). Moreover, when A is smooth and k is a characteristic zero field, we obtain a type of Hochschild-Kostant-Rosenberg theorem for these algebras. When A = k our complex reduce to the one obtained in [K] for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology.
Fil: Guccione, Jorge Alberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Guccione, Juan Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description We show that the Hochschild homology of a differential operator kalgebra E = A#f U(g), is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗A^-∗, b∗). Moreover, when A is smooth and k is a characteristic zero field, we obtain a type of Hochschild-Kostant-Rosenberg theorem for these algebras. When A = k our complex reduce to the one obtained in [K] for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology.
publishDate 2001
dc.date.none.fl_str_mv 2001-09
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/11336/110409
Guccione, Jorge Alberto; Guccione, Juan Jose; Hochschild (Co)Homology of Differential Operator Rings; Academic Press Inc Elsevier Science; Journal of Algebra; 243; 2; 9-2001; 596-614
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/110409
identifier_str_mv Guccione, Jorge Alberto; Guccione, Juan Jose; Hochschild (Co)Homology of Differential Operator Rings; Academic Press Inc Elsevier Science; Journal of Algebra; 243; 2; 9-2001; 596-614
0021-8693
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/pii/S0021869301988672
info:eu-repo/semantics/altIdentifier/doi/10.1006/jabr.2001.8867
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc 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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score 12.982451

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