arXiv subjects

Ruaa Jawad

Publications and source records attributed to Ruaa Jawad.

2 recordsLinked to original sources

arXiv2023

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

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.

math.KT↗

arXiv2020

Hochschild cohomology, finiteness conditions and a generalisation of $d$-Koszul algebras

Given a finite-dimensional algebra $Λ$ and $A \geqslant 1$, we construct a new algebra $\tildeΛ_A$, called the stretched algebra, and relate the homological properties of $Λ$ and $\tildeΛ_A$. We investigate Hochschild cohomology and the finiteness condition (Fg), and use stratifying ideals to show that $Λ$ has (Fg) if and only if $\tildeΛ_A$ has (Fg). We also consider projective resolutions and apply our results in the case where $Λ$ is a $d$-Koszul algebra for some $d \geqslant 2$.

math.RT↗