Hochschild (Co)homology of differential operators rings
- Autores
- Guccione, J.A.; Guccione, J.J.
- Año de publicación
- 2001
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We show that the Hochschild homology of a differential operator k-algebra E = A#fU(g) is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗ Ā* 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 reduces to the one obtained by C. Kassel (1988, Invent. Math. 91, 221-251) for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology. © 2001 Academic Press.
Fil:Guccione, J.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Guccione, J.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Fuente
- J. Algebra 2001;243(2):596-614
- Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
.jpg)
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_00218693_v243_n2_p596_Guccione
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Hochschild (Co)homology of differential operators ringsGuccione, J.A.Guccione, J.J.We show that the Hochschild homology of a differential operator k-algebra E = A#fU(g) is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗ Ā* 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 reduces to the one obtained by C. Kassel (1988, Invent. Math. 91, 221-251) for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology. © 2001 Academic Press.Fil:Guccione, J.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Guccione, J.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2001info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00218693_v243_n2_p596_GuccioneJ. Algebra 2001;243(2):596-614reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-23T11:18:35Zpaperaa:paper_00218693_v243_n2_p596_GuccioneInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-23 11:18:36.541Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
| dc.title.none.fl_str_mv |
Hochschild (Co)homology of differential operators rings |
| title |
Hochschild (Co)homology of differential operators rings |
| spellingShingle |
Hochschild (Co)homology of differential operators rings Guccione, J.A. |
| title_short |
Hochschild (Co)homology of differential operators rings |
| title_full |
Hochschild (Co)homology of differential operators rings |
| title_fullStr |
Hochschild (Co)homology of differential operators rings |
| title_full_unstemmed |
Hochschild (Co)homology of differential operators rings |
| title_sort |
Hochschild (Co)homology of differential operators rings |
| dc.creator.none.fl_str_mv |
Guccione, J.A. Guccione, J.J. |
| author |
Guccione, J.A. |
| author_facet |
Guccione, J.A. Guccione, J.J. |
| author_role |
author |
| author2 |
Guccione, J.J. |
| author2_role |
author |
| dc.description.none.fl_txt_mv |
We show that the Hochschild homology of a differential operator k-algebra E = A#fU(g) is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗ Ā* 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 reduces to the one obtained by C. Kassel (1988, Invent. Math. 91, 221-251) for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology. © 2001 Academic Press. Fil:Guccione, J.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Guccione, J.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
| description |
We show that the Hochschild homology of a differential operator k-algebra E = A#fU(g) is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in (M ⊗ Ā* 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 reduces to the one obtained by C. Kassel (1988, Invent. Math. 91, 221-251) for the homology of filtrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology. © 2001 Academic Press. |
| publishDate |
2001 |
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2001 |
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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 |
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http://hdl.handle.net/20.500.12110/paper_00218693_v243_n2_p596_Guccione |
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http://hdl.handle.net/20.500.12110/paper_00218693_v243_n2_p596_Guccione |
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eng |
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eng |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
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openAccess |
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http://creativecommons.org/licenses/by/2.5/ar |
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application/pdf |
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J. Algebra 2001;243(2):596-614 reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
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Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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