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Abstract:

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.

Registro:

Documento: Artículo
Título:Hochschild (Co)homology of differential operators rings
Autor:Guccione, J.A.; Guccione, J.J.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón 1- Ciudad Universitaria, Buenos Aires, Argentina
Año:2001
Volumen:243
Número:2
Página de inicio:596
Página de fin:614
DOI: http://dx.doi.org/10.1006/jabr.2001.8867
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v243_n2_p596_Guccione.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v243_n2_p596_Guccione

Referencias:

  • Blattner, R.J., Cohen, M., Montgomery, S., Crossed products and inner actions of Hopf algebras (1986) Trans. Amer. Math. Soc, 298, pp. 671-711
  • Borho, W., Gabriel, P., Rentschler, R., (1973) "Primideale in Einhüllenden Auflösbarer Lie-Algebren", 357. , Lecture Notes in Mathematics, Springer-Verlag, Berlin/Heidelberg/New York
  • Brylinski, J.L., A differential complex for Poisson manifolds (1988) J. Differential Geom, 28, pp. 93-114
  • Cap, A., Schichl, H., Vanzura, J., On twisted tensor products of algebras (1995) Comm. Algebra, 23, pp. 4701-4735
  • Chin, W., Prime ideals in differential operator rings and crossed products of infinite groups (1987) J. Algebra, 106, pp. 78-104
  • Doi, Y., Takeuchi, M., Cleft comodule algebras by a bialgebra (1986) Comm. Algebra, 14, pp. 801-817
  • Gerstenhaber, M., Schack, S.D., A Hodge-type decomposition for commutative algebra cohomology (1987) J. Pure Appl. Algebra, 48, pp. 229-247
  • Guccione, J.A., Guccione, J.J., Hochschild (co)homology of a Hopf crossed products K-theory, , to appear
  • Hochschild, G., Kostant, B., Rosenberg, A., Differential forms on regular affine algebras (1962) Trans. Amer. Math. Soc, 102, pp. 383-408
  • Kassel, C., L'homologie cyclique des algèbres enveloppantes (1988) Invent. Math, 91, pp. 221-251
  • Koszul, J.L., Crochet de Schouten-Nijenhuis et cohomologie (1985) "Colloque Elie Cartan", pp. 257-271. , Astérisque Hour Series, Soc. Math. France, Marseille
  • McConnell, J.C., Representations of solvable Lie algebras and the Gelfand-Kirillov conjecture (1974) Proc. London Math. Soc, 29, pp. 453-484
  • McConnell, J.C., Robson, J.C., (1987) "No Commutative Noetherian Rings", , Wiley-Interscience, New York
  • Montgomery, S., Crossed products of Hopf algebras and enveloping algebras (1988) "Perspectives in Ring Theory", pp. 253-268. , Kluwer Academic, Dordrecht
  • Sridharan, R., Filtered algebras and representations of Lie algebras (1961) Trans. Amer. Math. Soc, 100, pp. 530-550
  • Stefan, D., Hochschild cohomology of Hopf Galois extensions (1995) J. Pure Appl. Algebra, 103, pp. 221-233

Citas:

---------- APA ----------
Guccione, J.A. & Guccione, J.J. (2001) . Hochschild (Co)homology of differential operators rings. Journal of Algebra, 243(2), 596-614.
http://dx.doi.org/10.1006/jabr.2001.8867
---------- CHICAGO ----------
Guccione, J.A., Guccione, J.J. "Hochschild (Co)homology of differential operators rings" . Journal of Algebra 243, no. 2 (2001) : 596-614.
http://dx.doi.org/10.1006/jabr.2001.8867
---------- MLA ----------
Guccione, J.A., Guccione, J.J. "Hochschild (Co)homology of differential operators rings" . Journal of Algebra, vol. 243, no. 2, 2001, pp. 596-614.
http://dx.doi.org/10.1006/jabr.2001.8867
---------- VANCOUVER ----------
Guccione, J.A., Guccione, J.J. Hochschild (Co)homology of differential operators rings. J. Algebra. 2001;243(2):596-614.
http://dx.doi.org/10.1006/jabr.2001.8867