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arXiv · 1407.2661

Stacks of algebras and their homology

Nancy Heinschel·Birge Huisgen-Zimmermann
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Abstract

For any increasing function $f: {\Bbb N} \rightarrow {\Bbb N}_{\ge 2}$ 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.

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Nancy Heinschel, Birge Huisgen-Zimmermann. 2014-07-10. Stacks of algebras and their homology. https://arxiv.org/abs/1407.2661

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