{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KQ4DSMRJGCHWDCY7B7YXPKVIQG","short_pith_number":"pith:KQ4DSMRJ","schema_version":"1.0","canonical_sha256":"5438393229308f618b1f0ff177aaa88192048f371537e70c90128c6d7845a563","source":{"kind":"arxiv","id":"1701.06880","version":1},"attestation_state":"computed","paper":{"title":"Coset Vertex Operator Algebras and $\\W$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Cuipo Jiang, Tomoyuki Arakawa","submitted_at":"2017-01-24T14:08:17Z","abstract_excerpt":"We give an explicit description for the weight three generator of the coset vertex operator algebra $C_{L_{\\widehat{\\sl_{n}}}(l,0)\\otimes L_{\\widehat{\\sl_{n}}}(1,0)}(L_{\\widehat{\\sl_{n}}}(l+1,0))$, for $n\\geq 2, l\\geq 1$. Furthermore, we prove that the commutant $C_{L_{\\widehat{\\sl_{3}}}(l,0)\\otimes L_{\\widehat{\\sl_{3}}}(1,0)}(L_{\\widehat{\\sl_{3}}}(l+1,0))$ is isomorphic to the $\\W$-algebra $\\W_{-3+\\frac{l+3}{l+4}}(\\sl_3)$, which confirms the conjecture for the $\\sl_3$ case that $C_{L_{\\widehat{\\frak g}}(l,0)\\otimes L_{\\widehat{\\frak g}}(1,0)}(L_{\\widehat{\\frak g}}(l+1,0))$ is isomorphic to $\\"},"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":"1701.06880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-01-24T14:08:17Z","cross_cats_sorted":[],"title_canon_sha256":"f16a86e25c2cf50687a6e918158bfa73f070f11935ca68254bb1a44bdb819595","abstract_canon_sha256":"f71579253187ed22784e445f6c8fb6c9876148f026204074ad5d268344a0ec29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:10.243112Z","signature_b64":"l52Tulz585psUT8rxvTAABE30pXPFJEeqCJi1Jmf2sG19UkLcKcVxjXqHemxnRPf44mcvFj0kRQ3+3Ny5s+lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5438393229308f618b1f0ff177aaa88192048f371537e70c90128c6d7845a563","last_reissued_at":"2026-05-18T00:52:10.242564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:10.242564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coset Vertex Operator Algebras and $\\W$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Cuipo Jiang, Tomoyuki Arakawa","submitted_at":"2017-01-24T14:08:17Z","abstract_excerpt":"We give an explicit description for the weight three generator of the coset vertex operator algebra $C_{L_{\\widehat{\\sl_{n}}}(l,0)\\otimes L_{\\widehat{\\sl_{n}}}(1,0)}(L_{\\widehat{\\sl_{n}}}(l+1,0))$, for $n\\geq 2, l\\geq 1$. Furthermore, we prove that the commutant $C_{L_{\\widehat{\\sl_{3}}}(l,0)\\otimes L_{\\widehat{\\sl_{3}}}(1,0)}(L_{\\widehat{\\sl_{3}}}(l+1,0))$ is isomorphic to the $\\W$-algebra $\\W_{-3+\\frac{l+3}{l+4}}(\\sl_3)$, which confirms the conjecture for the $\\sl_3$ case that $C_{L_{\\widehat{\\frak g}}(l,0)\\otimes L_{\\widehat{\\frak g}}(1,0)}(L_{\\widehat{\\frak g}}(l+1,0))$ is isomorphic to $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06880","kind":"arxiv","version":1},"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":"1701.06880","created_at":"2026-05-18T00:52:10.242669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.06880v1","created_at":"2026-05-18T00:52:10.242669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06880","created_at":"2026-05-18T00:52:10.242669+00:00"},{"alias_kind":"pith_short_12","alias_value":"KQ4DSMRJGCHW","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KQ4DSMRJGCHWDCY7","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KQ4DSMRJ","created_at":"2026-05-18T12:31:24.725408+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/KQ4DSMRJGCHWDCY7B7YXPKVIQG","json":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG.json","graph_json":"https://pith.science/api/pith-number/KQ4DSMRJGCHWDCY7B7YXPKVIQG/graph.json","events_json":"https://pith.science/api/pith-number/KQ4DSMRJGCHWDCY7B7YXPKVIQG/events.json","paper":"https://pith.science/paper/KQ4DSMRJ"},"agent_actions":{"view_html":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG","download_json":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG.json","view_paper":"https://pith.science/paper/KQ4DSMRJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.06880&json=true","fetch_graph":"https://pith.science/api/pith-number/KQ4DSMRJGCHWDCY7B7YXPKVIQG/graph.json","fetch_events":"https://pith.science/api/pith-number/KQ4DSMRJGCHWDCY7B7YXPKVIQG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG/action/storage_attestation","attest_author":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG/action/author_attestation","sign_citation":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG/action/citation_signature","submit_replication":"https://pith.science/pith/KQ4DSMRJGCHWDCY7B7YXPKVIQG/action/replication_record"}},"created_at":"2026-05-18T00:52:10.242669+00:00","updated_at":"2026-05-18T00:52:10.242669+00:00"}