{"paper":{"title":"Truncated path algebras are homologically transparent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"A. Dugas, B. Huisgen-Zimmermann, J. Learned","submitted_at":"2014-07-10T01:33:42Z","abstract_excerpt":"It is shown that path algebras modulo relations of the form $\\Lambda = KQ/I$, where $Q$ is a quiver, $K$ a coefficient field, and $I \\subseteq KQ$ the ideal generated by all paths of a given length, can be readily analyzed homologically, while displaying a wealth of phenomena. In particular, the syzygies of their modules, and hence their finitistic dimensions, allow for smooth descriptions in terms of $Q$ and the Loewy length of $\\Lambda$. The same is true for the distributions of projective dimensions attained on the irreducible components of the standard parametrizing varieties for the modul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2672","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"}