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

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

2002-07-08

arxiv.org/abs/math/0207073v1

Journal of Pure and Applied Algebra, Volume 187, Issues 1-3 , 1 March 2004, Pages 255-294

Mathematics

Quantum Algebra

41 pages, article in french

Scientific paper

10.1016/S0022-4049(03)00146-4

We study Hochschild homology and cohomology for some polynomial algebras mixing both ``classical'' relations ($XY-YX=1$) and ``quantum'' relations ($XY={\l}YX$). 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.

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