The Ext Algebra and a New Generalization of D-Koszul Algebras

We generalize Koszul and D-Koszul algebras by introducing a class of graded algebras called (D, A)-stacked algebras. We give a characterization of (D, A)-stacked algebras, and show that their Ext algebra is finitely generated as an algebra in degrees 0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra by quiver and relations, and show that the ideal of relations has a quadratic Gröbner basis; this enables us to give a regrading of the Ext algebra under which the regraded Ext algebra is a Koszul algebra.