{"paper":{"title":"Minimal right determiners of irreducible morphisms in algebras of type ${\\mathbb A}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Xiaoxing Wu, Zhaoyong Huang","submitted_at":"2016-08-29T06:07:28Z","abstract_excerpt":"Let $\\Lambda$ be a finite dimensional algebra of type ${\\mathbb A}_n$ over an algebraically closed field $K$ with the quiver $Q$ and let $|\\Det(\\Lambda)|$ be the number of the minimal right determiners of all irreducible morphisms between indecomposable left $\\Lambda$-modules. If $\\Lambda$ is a path algebra, then we have $$|\\Det(\\Lambda)|= 2n-2, &\\mbox{if $p=0$; } 2n-p-1, &\\mbox{if $p\\geq 1$,}$$ where $p=|\\{i\\mid i$ is a source in $Q$ with $2\\leq i\\leq n-1\\}|$. If $\\Lambda$ is a bound quiver algebra, then we have $$ |\\Det(\\Lambda)|= 2n-2, &\\mbox{if $r=1$; } 2n-p-q-1, &\\mbox{if $r\\geq 2$,} $$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07918","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"}