{"paper":{"title":"Stacks of algebras and their homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Birge Huisgen-Zimmermann, Nancy Heinschel","submitted_at":"2014-07-10T00:54:57Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2661","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}