A COMBINATORIAL CHARACTERISATION OF d-KOSZUL AND (D,A)-STACKED MONOMIAL ALGEBRAS THAT SATISFY (Fg)

Abstract

Condition $\mathbf{\text{(Fg)}}$ was introduced in [6] to ensure that the theory of support varieties of a finite-dimensional algebra, established by Snashall and Solberg, has some similar properties to that of a group algebra. In this paper we give some easy-to-check combinatorial conditions that are equivalent to $\mathbf{\text{(Fg)}}$ for monomial $d$-Koszul algebras. We then extend this to monomial $(D,A)$-stacked algebras. We also extend the description of the Yoneda algebra of a $d$-Koszul algebra in [10] to $(D,A)$-stacked monomial algebras.