{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GFSF44RM7XTU4BFZMZDNKNVQ6K","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":"b57e2ef532e15fbd6fd0d49e38b4e42021d993d6e29a67bc72fadc5ea3f8d45a","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-21T15:44:56Z","title_canon_sha256":"793aa16bf3776c4961359b383031f3200d5f805ba68bd6512277a12624ea6864"},"schema_version":"1.0","source":{"id":"1509.06280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06280","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06280v1","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06280","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"GFSF44RM7XTU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GFSF44RM7XTU4BFZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GFSF44RM","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:de13ea855c87e00bd5dd2ea11a04c424d2f027b0977e54411b3a40d2c549b6ac","target":"graph","created_at":"2026-05-18T01:32:35Z","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":"Consider the W-algebra $W$ attached to the smallest nilpotent orbit in a simple Lie algebra $\\frak g$ over an algebraically closed field of characteristic 0. We show that if an analogue of the Gelfand-Kirillov conjecture holds for such a W-algebra then it holds for the universal enveloping algebra $\\mathrm U(\\frak g)$. This together with a result of A. Premet implies that the analogue of the Gelfand-Kirillov conjecture fails for some $W$-algebras attached to some nilpotent orbits in Lie algebras of types $B_n~(n\\ge 3)$, $D_n~(n\\ge 4)$, $E_6, E_7, E_8$, $F_4$.","authors_text":"Alexey Petukhov","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-21T15:44:56Z","title":"On Gelfand-Kirillov conjecture for some W-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06280","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":"sha256:5faec24ae56ad6d23f482b35fe6d44d39a80ea060e87ce8364cf46c65c9720a2","target":"record","created_at":"2026-05-18T01:32:35Z","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":"b57e2ef532e15fbd6fd0d49e38b4e42021d993d6e29a67bc72fadc5ea3f8d45a","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-21T15:44:56Z","title_canon_sha256":"793aa16bf3776c4961359b383031f3200d5f805ba68bd6512277a12624ea6864"},"schema_version":"1.0","source":{"id":"1509.06280","kind":"arxiv","version":1}},"canonical_sha256":"31645e722cfde74e04b96646d536b0f295e194894b44db9a62ab11ee0712cf5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31645e722cfde74e04b96646d536b0f295e194894b44db9a62ab11ee0712cf5f","first_computed_at":"2026-05-18T01:32:35.410019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:35.410019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vsQzg7blmy0lT1NbawcR1gSIBwGMlOpN58f4BUdlu1mahmJqxsOwTURZbkLAcLgGWwfeS6Gg2h0bXwF1NH4GDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:35.410503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5faec24ae56ad6d23f482b35fe6d44d39a80ea060e87ce8364cf46c65c9720a2","sha256:de13ea855c87e00bd5dd2ea11a04c424d2f027b0977e54411b3a40d2c549b6ac"],"state_sha256":"60bdc1e8d6f7a3342daa850f2079b33b2d3895bf8497e42452683eb89017cf35"}