Hochschild (Co)Homology of Differential Operator Rings

✍ Scribed by Jorge A Guccione; Juan J Guccione

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 164 KB
• Volume: 243
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8867

✦ Synopsis

We show that the Hochschild homology of a differential operator k-algebra E = A# f U g is the homology of a deformation of the Chevalley-Eilenberg complex of with coefficients in M ⊗ A * 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 1 Supported by UBACYT 01/TW79 and CONICET. We thank the referee for a substantial simplification in the proof of Theorem 3.1.1. 596