{"paper":{"title":"Semi-stable subcategories for Euclidean quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Charles Paquette, Colin Ingalls, Hugh Thomas","submitted_at":"2012-12-06T19:31:22Z","abstract_excerpt":"In this paper, we study the semi-stable subcategories of the category of representations of a Euclidean quiver, and the possible intersections of these subcategories. Contrary to the Dynkin case, we find out that the intersection of semi-stable subcategories may not be semi-stable. However, only a finite number of exceptions occur, and we give a description of these subcategories. Moreover, one can attach a simplicial fan in $\\mathbb{Q}^n$ to any acyclic quiver $Q$, and this simplicial fan allows one to completely determine the canonical presentation of any element in $\\mathbb{Z}^n$. This fan "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1424","kind":"arxiv","version":3},"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"}