{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WJJQXBAUBT2T2FLOSVYAEIZX5U","short_pith_number":"pith:WJJQXBAU","schema_version":"1.0","canonical_sha256":"b2530b84140cf53d156e9570022337ed294d27c56e7873ba7cc5398629d8487b","source":{"kind":"arxiv","id":"1903.00418","version":1},"attestation_state":"computed","paper":{"title":"On double quantum affinization: 1. Type $\\mathfrak a_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Elie Mounzer, Robin Zegers","submitted_at":"2019-03-01T17:17:16Z","abstract_excerpt":"We define the double quantum affinization $\\ddot{\\mathrm{U}}_q(\\mathfrak a_1)$ of type $\\mathfrak{a}_1$ as a topological Hopf algebra. We prove that it admits a subalgebra $\\ddot{\\mathrm{U}}_q'(\\mathfrak a_1)$ whose completion is (bicontinuously) isomorphic to the completion of the quantum toroidal algebra $\\dot{\\mathrm{U}}_q(\\dot{\\mathfrak a}_1)$, defined as the (simple) quantum affinization of the untwisted affine Kac-Moody Lie algebra $\\dot{\\mathfrak{sl}}_2$ of type $\\dot{\\mathfrak a}_1$, equipped with a certain topology inherited from its natural $\\mathbb Z$-grading. The isomorphism is con"},"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":"1903.00418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-03-01T17:17:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7ae23a959060597183f161d7727e434ee8fbe6f2a5889005ce5c2e78796dfede","abstract_canon_sha256":"6e8b4548beeae8f21de89b1e14dd9cec71df2ed68fd1e53dcdb9921ce0fa04e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:19.702738Z","signature_b64":"tE17Sxu2+oliFl+GckkKTIW9l77w29oiut1kiHQxZ+nvDaL/HKtklZrag1iGqPHq715icJW1dtxdq8lV8iTbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2530b84140cf53d156e9570022337ed294d27c56e7873ba7cc5398629d8487b","last_reissued_at":"2026-05-17T23:52:19.702036Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:19.702036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On double quantum affinization: 1. Type $\\mathfrak a_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Elie Mounzer, Robin Zegers","submitted_at":"2019-03-01T17:17:16Z","abstract_excerpt":"We define the double quantum affinization $\\ddot{\\mathrm{U}}_q(\\mathfrak a_1)$ of type $\\mathfrak{a}_1$ as a topological Hopf algebra. We prove that it admits a subalgebra $\\ddot{\\mathrm{U}}_q'(\\mathfrak a_1)$ whose completion is (bicontinuously) isomorphic to the completion of the quantum toroidal algebra $\\dot{\\mathrm{U}}_q(\\dot{\\mathfrak a}_1)$, defined as the (simple) quantum affinization of the untwisted affine Kac-Moody Lie algebra $\\dot{\\mathfrak{sl}}_2$ of type $\\dot{\\mathfrak a}_1$, equipped with a certain topology inherited from its natural $\\mathbb Z$-grading. The isomorphism is con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00418","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":"1903.00418","created_at":"2026-05-17T23:52:19.702135+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.00418v1","created_at":"2026-05-17T23:52:19.702135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00418","created_at":"2026-05-17T23:52:19.702135+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJJQXBAUBT2T","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJJQXBAUBT2T2FLO","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJJQXBAU","created_at":"2026-05-18T12:33:30.264802+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/WJJQXBAUBT2T2FLOSVYAEIZX5U","json":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U.json","graph_json":"https://pith.science/api/pith-number/WJJQXBAUBT2T2FLOSVYAEIZX5U/graph.json","events_json":"https://pith.science/api/pith-number/WJJQXBAUBT2T2FLOSVYAEIZX5U/events.json","paper":"https://pith.science/paper/WJJQXBAU"},"agent_actions":{"view_html":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U","download_json":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U.json","view_paper":"https://pith.science/paper/WJJQXBAU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.00418&json=true","fetch_graph":"https://pith.science/api/pith-number/WJJQXBAUBT2T2FLOSVYAEIZX5U/graph.json","fetch_events":"https://pith.science/api/pith-number/WJJQXBAUBT2T2FLOSVYAEIZX5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U/action/storage_attestation","attest_author":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U/action/author_attestation","sign_citation":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U/action/citation_signature","submit_replication":"https://pith.science/pith/WJJQXBAUBT2T2FLOSVYAEIZX5U/action/replication_record"}},"created_at":"2026-05-17T23:52:19.702135+00:00","updated_at":"2026-05-17T23:52:19.702135+00:00"}