{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3IUQQCKIQ64TSI2HTEY2FHGYIO","short_pith_number":"pith:3IUQQCKI","schema_version":"1.0","canonical_sha256":"da2908094887b93923479931a29cd843850494b6807616f0d8d84935c15e9e2d","source":{"kind":"arxiv","id":"1404.1738","version":2},"attestation_state":"computed","paper":{"title":"Elliptic Algebra U_{q,p}(g^) and Quantum Z-algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hitoshi Konno, Kazuyuki Oshima, Rasha M. Farghly","submitted_at":"2014-04-07T10:51:50Z","abstract_excerpt":"A new definition of the elliptic algebra U_{q,p}(g^) associated with an untwisted affine Lie algebra g^ is given as a topological algebra over the ring of formal power series in p. We also introduce a quantum dynamical analogue of Lepowsky-Wilson's Z-algebras. The Z-algebra governs the irreducibility of the infinite dimensional U_{q,p}(g^)-modules. Some level-1 examples indicate a direct connection of the irreducible U_{q,p}(g^)-modules to those of the W-algebras associated with the coset g^ \\oplus g^ \\supset (g^)_{diag} with level (r-g-1,1) (g:the dual Coxeter number), which includes Fateev- "},"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":"1404.1738","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2014-04-07T10:51:50Z","cross_cats_sorted":[],"title_canon_sha256":"eaf8508bc9b41e33d8f58e0e03d79af50972c313611488e1bc04d4acd05e5e16","abstract_canon_sha256":"b138434e3403f20d6e136503a29443d4cedc279fffb69e4e37dc267491285fc3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:44.180479Z","signature_b64":"/+b4gHnxRH61mVtESSqq1wrwh+mz1/qaBC3kMbJDCNmrN+J2FTPFw8RruVLAXI02L0NfxWWW6MPAD1D6grcJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da2908094887b93923479931a29cd843850494b6807616f0d8d84935c15e9e2d","last_reissued_at":"2026-05-18T02:47:44.179700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:44.179700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic Algebra U_{q,p}(g^) and Quantum Z-algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hitoshi Konno, Kazuyuki Oshima, Rasha M. Farghly","submitted_at":"2014-04-07T10:51:50Z","abstract_excerpt":"A new definition of the elliptic algebra U_{q,p}(g^) associated with an untwisted affine Lie algebra g^ is given as a topological algebra over the ring of formal power series in p. We also introduce a quantum dynamical analogue of Lepowsky-Wilson's Z-algebras. The Z-algebra governs the irreducibility of the infinite dimensional U_{q,p}(g^)-modules. Some level-1 examples indicate a direct connection of the irreducible U_{q,p}(g^)-modules to those of the W-algebras associated with the coset g^ \\oplus g^ \\supset (g^)_{diag} with level (r-g-1,1) (g:the dual Coxeter number), which includes Fateev- "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1738","kind":"arxiv","version":2},"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":"1404.1738","created_at":"2026-05-18T02:47:44.179823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1738v2","created_at":"2026-05-18T02:47:44.179823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1738","created_at":"2026-05-18T02:47:44.179823+00:00"},{"alias_kind":"pith_short_12","alias_value":"3IUQQCKIQ64T","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3IUQQCKIQ64TSI2H","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3IUQQCKI","created_at":"2026-05-18T12:28:11.866339+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/3IUQQCKIQ64TSI2HTEY2FHGYIO","json":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO.json","graph_json":"https://pith.science/api/pith-number/3IUQQCKIQ64TSI2HTEY2FHGYIO/graph.json","events_json":"https://pith.science/api/pith-number/3IUQQCKIQ64TSI2HTEY2FHGYIO/events.json","paper":"https://pith.science/paper/3IUQQCKI"},"agent_actions":{"view_html":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO","download_json":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO.json","view_paper":"https://pith.science/paper/3IUQQCKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1738&json=true","fetch_graph":"https://pith.science/api/pith-number/3IUQQCKIQ64TSI2HTEY2FHGYIO/graph.json","fetch_events":"https://pith.science/api/pith-number/3IUQQCKIQ64TSI2HTEY2FHGYIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO/action/storage_attestation","attest_author":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO/action/author_attestation","sign_citation":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO/action/citation_signature","submit_replication":"https://pith.science/pith/3IUQQCKIQ64TSI2HTEY2FHGYIO/action/replication_record"}},"created_at":"2026-05-18T02:47:44.179823+00:00","updated_at":"2026-05-18T02:47:44.179823+00:00"}