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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| Autores principales: | , |
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| Publicado: |
2001
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v243_n2_p596_Guccione http://hdl.handle.net/20.500.12110/paper_00218693_v243_n2_p596_Guccione |
| Aporte de: |
| Sumario: | 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. |
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