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: Guccione, Jorge Alberto, Guccione, Juan José
Publicado: 2001
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
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00218693_v243_n2_p596_Guccione2023-06-08T14:42:20Z Hochschild (Co)homology of differential operators rings Guccione, Jorge Alberto Guccione, Juan José 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 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
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
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.
author Guccione, Jorge Alberto
Guccione, Juan José
spellingShingle Guccione, Jorge Alberto
Guccione, Juan José
Hochschild (Co)homology of differential operators rings
author_facet Guccione, Jorge Alberto
Guccione, Juan José
author_sort Guccione, Jorge Alberto
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 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
work_keys_str_mv AT guccionejorgealberto hochschildcohomologyofdifferentialoperatorsrings
AT guccionejuanjose hochschildcohomologyofdifferentialoperatorsrings
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