{"paper":{"title":"Classifying representations by way of Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Birge Huisgen-Zimmermann","submitted_at":"2014-07-10T01:04:03Z","abstract_excerpt":"Let $\\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\\Lambda$ with fixed dimension $d$ and fixed squarefree top $T$. Next to providing a complete theoretical picture, some of these equivalent conditions are readily checkable from quiver and relations. In case of existence of a moduli space -- unexpectedly frequent in light of the stringency of fine classification -- this space is always projective and, in fact, arises as a closed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2664","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"}