{"paper":{"title":"Structures and Representations of Generalized Path Algebras","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Shouchuan Zhang, Yao-Zhong Zhang","submitted_at":"2004-02-12T00:13:43Z","abstract_excerpt":"It is shown that an algebra $\\Lambda $ can be lifted with nilpotent Jacobson radical $r = r(\\Lambda)$ and has a generalized matrix unit $\\{e_{ii}\\}_I$ with each $\\bar e_{ii} $ in the center of $\\bar \\Lambda = \\Lambda /r$ iff $\\Lambda $ is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path algebras are given. As a corollary, $\\Lambda $ is a finite algebra with non-zero unity element over perfect field $k$ (e.g. a field with characteristic zero or a finite field) iff $\\Lambda $ is isomorphic to a generalized path algebra $k (D, \\Omega, \\rho)$ of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402188","kind":"arxiv","version":5},"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"}