Hochschild (Co)homology of differential operators rings
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-Ros...
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2001
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00218693_v243_n2_p596_Guccione |
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paperaa:paper_00218693_v243_n2_p596_Guccione2023-06-12T16:42:21Z Hochschild (Co)homology of differential operators rings J. Algebra 2001;243(2):596-614 Guccione, 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. 2001 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00218693_v243_n2_p596_Guccione |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| 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. |
| format |
Artículo Artículo publishedVersion |
| author |
Guccione, J.A. Guccione, J.J. |
| spellingShingle |
Guccione, J.A. Guccione, J.J. Hochschild (Co)homology of differential operators rings |
| author_facet |
Guccione, J.A. Guccione, J.J. |
| author_sort |
Guccione, J.A. |
| title |
Hochschild (Co)homology of differential operators rings |
| 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 |
| publishDate |
2001 |
| url |
http://hdl.handle.net/20.500.12110/paper_00218693_v243_n2_p596_Guccione |
| work_keys_str_mv |
AT guccioneja hochschildcohomologyofdifferentialoperatorsrings AT guccionejj hochschildcohomologyofdifferentialoperatorsrings |
| _version_ |
1769810372985880576 |