Hochschild homology and cohomology of some classical and quantum noncommutative polynomial algebras

✍ Scribed by Lionel Richard

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 499 KB
• Volume: 187
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(03)00146-4

✦ Synopsis

We study Hochschild homology and cohomology for a class of noncommutative polynomial algebras which are both quantum (in the sense that they contain some copies of Manin's quantum plane as subalgebras) and classical (in the sense that they also contain some copies of the Weyl algebra A1). We obtain explicit computations for some signiÿcant families of such algebras. In particular, we prove that the algebra of twisted di erential operators on a quantum a ne space (simple quantum Weyl algebra) has the same Hochschild homology, and satisÿes the same duality relation, as the classical Weyl algebra does.