{"paper":{"title":"Finite Dimensional Representations of Leavitt Path Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Ayten Ko\\c{c}, Murad \\\"Ozayd{\\i}n","submitted_at":"2016-07-15T19:29:29Z","abstract_excerpt":"When $\\Gamma$ is a row-finite di(rected )graph we classify all finite dimensional modules of the Leavitt path algebra $L(\\Gamma)$ via an explicit Morita equivalence given by an effective combinatorial (reduction) algorithm on the digraph $\\Gamma$. The category of (unital) $L(\\Gamma)$-modules is equivalent to a subcategory of quiver representations of $\\Gamma$. However the category of finite dimensional representations of $L(\\Gamma)$ is tame in contrast to the finite dimensional quiver representations of $\\Gamma$ which are almost always wild."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04622","kind":"arxiv","version":2},"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"}