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
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- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/110409
Ver los metadatos del registro completo
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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 |
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article |
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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 |
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eng |
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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 |
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info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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application/pdf application/pdf application/pdf |
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Academic Press Inc Elsevier Science |
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Academic Press Inc Elsevier Science |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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