Stacks of algebras and their homology
Nancy Heinschel, Birge Huisgen-Zimmermann

TL;DR
This paper constructs finite dimensional algebras with prescribed finitistic dimensions using a stacking technique, enabling precise control over their homological properties and higher syzygies.
Contribution
It introduces a novel stacking method to build algebras with specific finitistic dimension functions, advancing the understanding of homological dimensions.
Findings
Constructed algebras with finitistic dimension functions matching any finite-valued increasing function.
Developed a stacking technique to control higher syzygies of modules.
Provided new examples illustrating the range of finitistic dimensions.
Abstract
For any increasing function which takes only finitely many distinct values, a connected finite dimensional algebra is constructed, with the property that for all ; here is the -generated finitistic dimension of . The stacking technique developed for this construction of homological examples permits strong control over the higher syzygies of -modules in terms of the algebras serving as layers.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications
