{"paper":{"title":"Path algebras of quivers and representations of locally finite Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"J. Hennig, S. J. Sierra","submitted_at":"2015-12-28T10:05:04Z","abstract_excerpt":"We explore the (noncommutative) geometry of locally simple representations of the diagonal locally finite Lie algebras $\\mathfrak{sl}(n^\\infty)$, $\\mathfrak o(n^\\infty)$, and $\\mathfrak{sp}(n^\\infty)$. Let $\\mathfrak g_\\infty$ be one of these Lie algebras, and let $I \\subseteq U(\\mathfrak g_\\infty)$ be the nonzero annihilator of a locally simple $\\mathfrak g_\\infty$-module. We show that for each such $I$, there is a quiver $Q$ so that locally simple $\\mathfrak g_\\infty$-modules with annihilator $I$ are parameterised by \"points\" in the \"noncommutative space\" corresponding to the path algebra of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08362","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"}