Homologie et cohomologie de Hochschild de certaines algebres polynomiales classiques et quantiques

Abstract

We study Hochschild homology and cohomology for some polynomial algebras mixing both ``classical'' relations ($XY-YX=1$) and ``quantum'' relations ($XY=łYX$). More specifically, we prove that the algebra of differential operators on any quantum affine space (quantum Weyl algebra) have the same Hochschild homology, and satisfy the same duality relation, as the classical Weyl algebra does.

arXiv comment41 pages, article in french

References in corpus (1)

• Hochschild homology and cohomology of generalized Weyl algebras

Cited by in corpus (4)

• Twisted Poincare duality for some quadratic Poisson algebras
• On deformations of $A_{\infty }$-algebras
• Equivalence rationnelle d'algebres polynomiales classiques et quantiques
• Hochschild cohomology of group extensions of quantum symmetric algebras