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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.08362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-28T10:05:04Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"8e938bb12b9d69fea6e462a638607c36ce96ea702d4f82733649be0825c80e9e","abstract_canon_sha256":"f56e88c1a0e9223b9b5305aee738c86d7f26f094ba57d33620cd3ca0f27a422b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:22.685183Z","signature_b64":"Ll+ouWFXLVHdjB2ZiwxYvC5oKdBygp9uN9B6KIBrQb7RztbkJD1UsSI1DIy1T+qwJIRRV3/P7G5a1PG0mwyzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"367a646472f9f39e66601472d720b5e77d64fc2868e5b86b5c019d5eda1da038","last_reissued_at":"2026-05-18T01:12:22.684831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:22.684831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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