Finite Generation of Ext and (D,A)-stacked Algebras

We introduce the class of (D,A)-stacked algebras, which generalise the classes of Koszul algebras, d-Koszul algebras and (D,A)-stacked monomial algebras. We show that the Ext algebra of a (D,A)-stacked algebra is finitely generated in degrees 0, 1, 2 and 3. After investigating some general properties of E(Ʌ) for this class of algebras, we look at a regrading of E(Ʌ) and give examples for which the regraded Ext algebra is a Koszul algebra. Following this we give a general construction of a (D,A)-stacked algebra ~Ʌ from a d-Koszul algebra Ʌ, setting D = dA, with A ≥ 1. From this construction we relate the homological properties of ~Ʌ and Ʌ, including the projective resolutions and the structure of the Ext algebra.