Koszulity for Nonquadratic Algebras

It is known that a Koszul algebra is defined as being a quadratic algebra with a “pure” resolution of the ground field. In this paper, we extend Koszulity to algebras whose relations are homogeneous of degree s > 2. A cubic Artin–Schelter regular algebra has motivated our work. Generalized Koszulity is connected to lattice distributivity and to confluence. A generalized symmetric algebra is proved to be generalized Koszul, and the bimodule version of the generalized Koszul resolution is used for investigating its Hochschild homology.