Homologies of cubic Artin-Schelter regular algebras
The author computes the Hochschild homology of Artin-Schelter regular algebras with global dimension 3 and cubic relations. Let us recall that the Hochschild homology of AS-regular algebras were already computed in the case of quadratic relations. Here, the author considers the case of cubic relations and generic coefficients. The main idea used is to see these algebras as deformations of a polynomial algebra equipped with a Poisson structure. Finally, the Hochschild cohomology is also studied and a Poincaré duality is obtained.
scientific article; zbMATH DE number 2105349