{"paper":{"title":"Homogeneity implies Tameness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yingbo Zhang, Yunge Xu","submitted_at":"2014-03-24T12:16:11Z","abstract_excerpt":"Let $\\Lambda$ be a finite-dimensional basic algebra over an algebraically closed field $k$. The well-known Drozd's theorem asserts, that $\\Lambda$ is either tame or wild. The Crawley-Boevey's Theorem states that for a given tame algebra $\\Lambda$, and for each dimension $d$ almost all isomorphism classes of indecomposable $\\Lambda$-modules of dimension $d$ are isomorphic to their Auslander-Reiten translations and hence belong to homogeneous tubes. In this paper we prove the converse of Crawley-Boevey's Theorem and thus give an internal description of tameness in terms of AR-quivers. This gives"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5930","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"}