A combinatorial characterisation of d-Koszul and (D,A)-stacked monomial algebras that satisfy (Fg)

TL;DR

This paper provides combinatorial criteria to determine when monomial d-Koszul and (D,A)-stacked algebras satisfy the (Fg) condition, linking algebraic properties to combinatorial structures.

Contribution

It introduces easy-to-check combinatorial conditions for (Fg) in monomial d-Koszul and (D,A)-stacked algebras, extending previous descriptions of their Yoneda algebras.

Findings

Combinatorial conditions equivalent to (Fg) for monomial d-Koszul algebras

Extension of (Fg) criteria to monomial (D,A)-stacked algebras

Extended description of the Yoneda algebra for (D,A)-stacked monomial algebras

Abstract

Condition (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 (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 [11] to (D, A)-stacked monomial algebras.