Stacks of algebras and their homology

Abstract

For any increasing function $f:\mathbb{N}\to {\mathbb{N}}_{\ge 2}$ which takes only finitely many distinct values, a connected finite dimensional algebra $\Lambda$ is constructed, with the property that ${\text{fin.dim}}_n\Lambda =f(n)$ for all $n$; here ${\text{fin.dim}}_n\Lambda$ is the $n$-generated finitistic dimension of $\Lambda$. The stacking technique developed for this construction of homological examples permits strong control over the higher syzygies of $\Lambda$-modules in terms of the algebras serving as layers.