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

Abstract

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

References in corpus (1)

• Support varieties for selfinjective algebras