{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VQVRAP4CWQ4IMO57BPIM775CCB","short_pith_number":"pith:VQVRAP4C","schema_version":"1.0","canonical_sha256":"ac2b103f82b438863bbf0bd0cfffa21044fcabe627b8b28d2d41193bf7ea0339","source":{"kind":"arxiv","id":"1301.4653","version":3},"attestation_state":"computed","paper":{"title":"Derived subalgebras of centralisers and finite W-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Alexander Premet, Lewis Topley","submitted_at":"2013-01-20T12:14:52Z","abstract_excerpt":"Let g = Lie(G) be the Lie algebra of a simple algebraic group G over an algebraically closed field of characteristic 0. Let e be a nilpotent element of g and let g_e = Lie(G_e) where G_e stands for the stabiliser of e in G. For g classical, we give an explicit combinatorial formula for the codimension of [g_e, g_e] in g_e and use it to determine those e in g for which the largest commutative quotient U(g,e)^{ab} of the finite W-algebra U(g,e) is isomorphic to a polynomial algebra. It turns out that this happens if and only if e lies in a unique sheet of g. The nilpotent elements with this prop"},"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":"1301.4653","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-20T12:14:52Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"0dbb85f11c7761c0fc250ed564d173ce5a4e38ea3aa4f49c014bf1e02f0f0668","abstract_canon_sha256":"773946d7b445bc1e99aa6055e87b257ef9d40fe6470c45bc917d29dd0ea90572"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:31.903597Z","signature_b64":"KfJmBizZ+DtO99bUsBrrq9OF1wl//v0Jce7b7CUP9JCHaLfu13+R4lrwUYK7etzui6WDzTwK5OLOegMD0M8HDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac2b103f82b438863bbf0bd0cfffa21044fcabe627b8b28d2d41193bf7ea0339","last_reissued_at":"2026-05-18T02:47:31.903131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:31.903131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derived subalgebras of centralisers and finite W-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Alexander Premet, Lewis Topley","submitted_at":"2013-01-20T12:14:52Z","abstract_excerpt":"Let g = Lie(G) be the Lie algebra of a simple algebraic group G over an algebraically closed field of characteristic 0. Let e be a nilpotent element of g and let g_e = Lie(G_e) where G_e stands for the stabiliser of e in G. For g classical, we give an explicit combinatorial formula for the codimension of [g_e, g_e] in g_e and use it to determine those e in g for which the largest commutative quotient U(g,e)^{ab} of the finite W-algebra U(g,e) is isomorphic to a polynomial algebra. It turns out that this happens if and only if e lies in a unique sheet of g. The nilpotent elements with this prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4653","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":""},"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":"1301.4653","created_at":"2026-05-18T02:47:31.903197+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4653v3","created_at":"2026-05-18T02:47:31.903197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4653","created_at":"2026-05-18T02:47:31.903197+00:00"},{"alias_kind":"pith_short_12","alias_value":"VQVRAP4CWQ4I","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VQVRAP4CWQ4IMO57","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VQVRAP4C","created_at":"2026-05-18T12:28:04.890932+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/VQVRAP4CWQ4IMO57BPIM775CCB","json":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB.json","graph_json":"https://pith.science/api/pith-number/VQVRAP4CWQ4IMO57BPIM775CCB/graph.json","events_json":"https://pith.science/api/pith-number/VQVRAP4CWQ4IMO57BPIM775CCB/events.json","paper":"https://pith.science/paper/VQVRAP4C"},"agent_actions":{"view_html":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB","download_json":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB.json","view_paper":"https://pith.science/paper/VQVRAP4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4653&json=true","fetch_graph":"https://pith.science/api/pith-number/VQVRAP4CWQ4IMO57BPIM775CCB/graph.json","fetch_events":"https://pith.science/api/pith-number/VQVRAP4CWQ4IMO57BPIM775CCB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB/action/storage_attestation","attest_author":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB/action/author_attestation","sign_citation":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB/action/citation_signature","submit_replication":"https://pith.science/pith/VQVRAP4CWQ4IMO57BPIM775CCB/action/replication_record"}},"created_at":"2026-05-18T02:47:31.903197+00:00","updated_at":"2026-05-18T02:47:31.903197+00:00"}