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A subalgebra $\\mathfrak{l}\\subset\\mathfrak{g}$ for which there exists an irreducible module $M$ with $\\mathfrak{g}[M]=\\mathfrak{l}$ is called a Fernando-Kac subalgebra of $\\mathfrak{g}$. A Fernando-Kac subalgebra of $\\mathfrak{g}$ is of finite type if in addition $M$ can be chosen to have finite Jordan-H\\\"older $\\mathfrak{"},"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":"1009.5260","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-09-27T14:10:26Z","cross_cats_sorted":[],"title_canon_sha256":"ce849b6104bb71143d6230b76779c91c31ca99074ae6ed3a8cda24f8d2fc278c","abstract_canon_sha256":"ce2c36af7cf5a65691b814cdd591db5343d87d1db07768c46fc70987f44db8d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:38.085306Z","signature_b64":"v1yDv+ZIFav+0est1dIZtuROKjSFEGaGAsS+YeInkn69+eGxv2b5DF1g9+f4XbW9S4S2p7vSJoX6x8x+/qN1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0019f2f8d25e1d2e94b70a85298906254daa9895c6aeedbb6a7690276c42c86d","last_reissued_at":"2026-05-18T04:14:38.084848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:38.084848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Root Fernando-Kac subalgebras of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Todor Milev","submitted_at":"2010-09-27T14:10:26Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a finite-dimensional Lie algebra and $M$ be a $\\mathfrak{g}$-module. The Fernando-Kac subalgebra of $\\mathfrak{g}$ associated to $M$ is the subset $\\mathfrak{g}[M]\\subset\\mathfrak{g}$ of all elements $g\\in\\mathfrak{g}$ which act locally finitely on $M$. A subalgebra $\\mathfrak{l}\\subset\\mathfrak{g}$ for which there exists an irreducible module $M$ with $\\mathfrak{g}[M]=\\mathfrak{l}$ is called a Fernando-Kac subalgebra of $\\mathfrak{g}$. A Fernando-Kac subalgebra of $\\mathfrak{g}$ is of finite type if in addition $M$ can be chosen to have finite Jordan-H\\\"older $\\mathfrak{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5260","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.5260","created_at":"2026-05-18T04:14:38.084923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.5260v4","created_at":"2026-05-18T04:14:38.084923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5260","created_at":"2026-05-18T04:14:38.084923+00:00"},{"alias_kind":"pith_short_12","alias_value":"AAM7F6GSLYOS","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AAM7F6GSLYOS5FFX","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AAM7F6GS","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV","json":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV.json","graph_json":"https://pith.science/api/pith-number/AAM7F6GSLYOS5FFXBKCSTCIGEV/graph.json","events_json":"https://pith.science/api/pith-number/AAM7F6GSLYOS5FFXBKCSTCIGEV/events.json","paper":"https://pith.science/paper/AAM7F6GS"},"agent_actions":{"view_html":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV","download_json":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV.json","view_paper":"https://pith.science/paper/AAM7F6GS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.5260&json=true","fetch_graph":"https://pith.science/api/pith-number/AAM7F6GSLYOS5FFXBKCSTCIGEV/graph.json","fetch_events":"https://pith.science/api/pith-number/AAM7F6GSLYOS5FFXBKCSTCIGEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV/action/storage_attestation","attest_author":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV/action/author_attestation","sign_citation":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV/action/citation_signature","submit_replication":"https://pith.science/pith/AAM7F6GSLYOS5FFXBKCSTCIGEV/action/replication_record"}},"created_at":"2026-05-18T04:14:38.084923+00:00","updated_at":"2026-05-18T04:14:38.084923+00:00"}