Hochschild (co)homology of differential operator rings

JORGE GUCCIONE; JUAN JOSÉ GUCCIONE

JOURNAL OF ALGEBRA

Año: 2001 vol. 243 p. 596 - 614

0021-8693

We show that the Hochschild homology of a differential operator k- algebra E = A#fU(g) with coefficients in am A-bimodule M, is the homology of a deformation of the Chevalley-Eilenberg complex of g with coefficients in the tensor produc on A of M with the normalized Hochschild complex of A. 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 reduce to the one obtained in [K] for the homology of fltrated algebras whose associated graded algebras are symmetric algebras. In the last section we give similar results for the cohomology.