{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LOKBBRHMKUIOXLFLE7PPRJA6II","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"395edc24b68854d243e3dbc0e9e819ca8406ce6686a6ccbc88e74ddf66683f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-19T07:41:46Z","title_canon_sha256":"a9b231eee570d4289b792b20a38237a1da1d1acf9c6afa95bc278d122cf46169"},"schema_version":"1.0","source":{"id":"1502.05486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05486","created_at":"2026-05-18T02:26:46Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05486v1","created_at":"2026-05-18T02:26:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05486","created_at":"2026-05-18T02:26:46Z"},{"alias_kind":"pith_short_12","alias_value":"LOKBBRHMKUIO","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOKBBRHMKUIOXLFL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOKBBRHM","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:7cabe70da0f470191c8eea4b437650c98b30eab3eb8d78a63219a18afabed8d0","target":"graph","created_at":"2026-05-18T02:26:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the center of $U(\\mathfrak{n})$, where $\\mathfrak{n}$ is the locally nilpotent radical of a splitting Borel subalgebra of a simple complex Lie algebra $\\mathfrak{g}=\\mathfrak{sl}_{\\infty}(\\mathbb{C})$, $\\mathfrak{so}_{\\infty}(\\mathbb{C})$, $\\mathfrak{sp}_{\\infty}(\\mathbb{C})$. There are infinitely many isomorphism classes of Lie algebras $\\mathfrak{n}$, and we provide explicit generators of the center of $U(\\mathfrak{n})$ in all cases. We then fix $\\mathfrak{n}$ with \"largest possible\" center of $U(\\mathfrak{n})$ and characterize the centrally generated primitive ideals of $U(\\mathfra","authors_text":"Ivan Penkov, Mikhail Ignatyev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-19T07:41:46Z","title":"Infinite Kostant cascades and centrally generated primitive ideals of $U(\\mathfrak{n})$ in types $A_{\\infty}$, $C_{\\infty}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05486","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fd9ac5424c2afa63898addf657189372dd37a98cf21a1f460c858814e8a4a1c4","target":"record","created_at":"2026-05-18T02:26:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"395edc24b68854d243e3dbc0e9e819ca8406ce6686a6ccbc88e74ddf66683f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-19T07:41:46Z","title_canon_sha256":"a9b231eee570d4289b792b20a38237a1da1d1acf9c6afa95bc278d122cf46169"},"schema_version":"1.0","source":{"id":"1502.05486","kind":"arxiv","version":1}},"canonical_sha256":"5b9410c4ec5510ebacab27def8a41e422ee50215ff22c1692a3a72b0bba3d00f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b9410c4ec5510ebacab27def8a41e422ee50215ff22c1692a3a72b0bba3d00f","first_computed_at":"2026-05-18T02:26:46.411329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:46.411329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G2saags0G9283C/BU5JvEqqE2fER/J59qUZgW/Pd17dw2EgoASvv93ENjTfjXDqCQm8vXLRfujT5P405wM8gCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:46.411876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd9ac5424c2afa63898addf657189372dd37a98cf21a1f460c858814e8a4a1c4","sha256:7cabe70da0f470191c8eea4b437650c98b30eab3eb8d78a63219a18afabed8d0"],"state_sha256":"bc4f897bd75eec96454f6fb58b125afa98705336c38089328b07e38c9dad02ad"}