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If $\\lambda \\neq 0$ then $U_\\lambda(L)$ is simple.\n  Theorem 2. The algebra $U_0(L)$ has just-infinite growth, in the sense that any proper quotient has polynomial growth.\n  As an immediate corollary, we show that the annihilator of any nontrivial integrable highest weight representation of $L$ is centrally generated, extending a result of Chari f"},"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":"2112.08334","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2021-12-15T18:31:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9aa69e0db443a63ab3e8e95e490b043ab6681ed48ec6b6adf56b86ce91151824","abstract_canon_sha256":"b8ed2c8052683a3cd780070a141b48e351f4992b62321729f4e43ec21a7ca55f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:06.352594Z","signature_b64":"n9Ez+vh/VJEtsFxorYjy25WhF2xKMk5WjCe1QgriIOIaCvk2HWdg8QhzeNIypDZdZFl38kYWfsDAPUBSdEmYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"135d6ef9293d3708cef267ffb7088d1198fc33fb100c6428ecc53ab828d5208d","last_reissued_at":"2026-07-05T11:06:06.352040Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:06.352040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideals in enveloping algebras of affine Kac-Moody algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Rekha Biswal, Susan J. Sierra","submitted_at":"2021-12-15T18:31:22Z","abstract_excerpt":"Let $L$ be an affine Kac-Moody algebra, with central element $c$, and let $\\lambda \\in \\mathbb C$. We study two-sided ideals in the central quotient $U_\\lambda(L):= U(L)/(c-\\lambda)$ of the universal enveloping algebra of $L$, and prove:\n  Theorem 1. If $\\lambda \\neq 0$ then $U_\\lambda(L)$ is simple.\n  Theorem 2. The algebra $U_0(L)$ has just-infinite growth, in the sense that any proper quotient has polynomial growth.\n  As an immediate corollary, we show that the annihilator of any nontrivial integrable highest weight representation of $L$ is centrally generated, extending a result of Chari f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.08334","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.08334/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2112.08334","created_at":"2026-07-05T11:06:06.352104+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.08334v3","created_at":"2026-07-05T11:06:06.352104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.08334","created_at":"2026-07-05T11:06:06.352104+00:00"},{"alias_kind":"pith_short_12","alias_value":"CNOW56JJHU3Q","created_at":"2026-07-05T11:06:06.352104+00:00"},{"alias_kind":"pith_short_16","alias_value":"CNOW56JJHU3QRTXS","created_at":"2026-07-05T11:06:06.352104+00:00"},{"alias_kind":"pith_short_8","alias_value":"CNOW56JJ","created_at":"2026-07-05T11:06:06.352104+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.17972","citing_title":"Enveloping algebras of derivations of commutative and noncommutative algebras","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG","json":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG.json","graph_json":"https://pith.science/api/pith-number/CNOW56JJHU3QRTXSM773OCENCG/graph.json","events_json":"https://pith.science/api/pith-number/CNOW56JJHU3QRTXSM773OCENCG/events.json","paper":"https://pith.science/paper/CNOW56JJ"},"agent_actions":{"view_html":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG","download_json":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG.json","view_paper":"https://pith.science/paper/CNOW56JJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.08334&json=true","fetch_graph":"https://pith.science/api/pith-number/CNOW56JJHU3QRTXSM773OCENCG/graph.json","fetch_events":"https://pith.science/api/pith-number/CNOW56JJHU3QRTXSM773OCENCG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG/action/storage_attestation","attest_author":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG/action/author_attestation","sign_citation":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG/action/citation_signature","submit_replication":"https://pith.science/pith/CNOW56JJHU3QRTXSM773OCENCG/action/replication_record"}},"created_at":"2026-07-05T11:06:06.352104+00:00","updated_at":"2026-07-05T11:06:06.352104+00:00"}