{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ITI2XNID7U4XY2D2W3CV3SV6WB","short_pith_number":"pith:ITI2XNID","schema_version":"1.0","canonical_sha256":"44d1abb503fd397c687ab6c55dcabeb07df6456beebf55faf3ca483aaf382a77","source":{"kind":"arxiv","id":"1601.01377","version":3},"attestation_state":"computed","paper":{"title":"Combinatorial aspects of the quantized universal enveloping algebra of $\\mathfrak{sl}_{n+1}(\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"David M. Jackson, Geoffrey Stanley, Raymond Cheng","submitted_at":"2016-01-07T02:42:19Z","abstract_excerpt":"Quasi-triangular Hopf algebras were introduced by Drinfel'd in his construction of solutions to the Yang--Baxter Equation. This algebra is built upon $\\mathcal{U}_h(\\mathfrak{sl}_2)$, the quantized universal enveloping algebra of the Lie algebra $\\mathfrak{sl}_2$. In this paper, combinatorial structure in $\\mathcal{U}_h(\\mathfrak{sl}_2)$ is elicited, and used to assist in highly intricate calculations in this algebra. To this end, a combinatorial methodology is formulated for straightening algebraic expressions to a canonical form in the case $n=1$. We apply this formalism to the quasi-triangu"},"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":"1601.01377","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-07T02:42:19Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"8ec864bd09006aef9dde27e6d96f77b76b1385ca9d4233da97fac348a222945f","abstract_canon_sha256":"0c803bf01949e460003f74d0c6a2de9a54de7153d21ed8d526a16d69557daa24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:19.434285Z","signature_b64":"8W/t5lUtfVsvEtzfJ/uoS61uqFb9btNP7k7urf2EXzCTQWFXHUfrk/eEAyPWfPULiCDR8DAK9GBf6D0E+ZfWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44d1abb503fd397c687ab6c55dcabeb07df6456beebf55faf3ca483aaf382a77","last_reissued_at":"2026-05-18T00:11:19.433616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:19.433616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial aspects of the quantized universal enveloping algebra of $\\mathfrak{sl}_{n+1}(\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"David M. Jackson, Geoffrey Stanley, Raymond Cheng","submitted_at":"2016-01-07T02:42:19Z","abstract_excerpt":"Quasi-triangular Hopf algebras were introduced by Drinfel'd in his construction of solutions to the Yang--Baxter Equation. This algebra is built upon $\\mathcal{U}_h(\\mathfrak{sl}_2)$, the quantized universal enveloping algebra of the Lie algebra $\\mathfrak{sl}_2$. In this paper, combinatorial structure in $\\mathcal{U}_h(\\mathfrak{sl}_2)$ is elicited, and used to assist in highly intricate calculations in this algebra. To this end, a combinatorial methodology is formulated for straightening algebraic expressions to a canonical form in the case $n=1$. We apply this formalism to the quasi-triangu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01377","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":"1601.01377","created_at":"2026-05-18T00:11:19.433724+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.01377v3","created_at":"2026-05-18T00:11:19.433724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01377","created_at":"2026-05-18T00:11:19.433724+00:00"},{"alias_kind":"pith_short_12","alias_value":"ITI2XNID7U4X","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"ITI2XNID7U4XY2D2","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"ITI2XNID","created_at":"2026-05-18T12:30:22.444734+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/ITI2XNID7U4XY2D2W3CV3SV6WB","json":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB.json","graph_json":"https://pith.science/api/pith-number/ITI2XNID7U4XY2D2W3CV3SV6WB/graph.json","events_json":"https://pith.science/api/pith-number/ITI2XNID7U4XY2D2W3CV3SV6WB/events.json","paper":"https://pith.science/paper/ITI2XNID"},"agent_actions":{"view_html":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB","download_json":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB.json","view_paper":"https://pith.science/paper/ITI2XNID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.01377&json=true","fetch_graph":"https://pith.science/api/pith-number/ITI2XNID7U4XY2D2W3CV3SV6WB/graph.json","fetch_events":"https://pith.science/api/pith-number/ITI2XNID7U4XY2D2W3CV3SV6WB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB/action/storage_attestation","attest_author":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB/action/author_attestation","sign_citation":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB/action/citation_signature","submit_replication":"https://pith.science/pith/ITI2XNID7U4XY2D2W3CV3SV6WB/action/replication_record"}},"created_at":"2026-05-18T00:11:19.433724+00:00","updated_at":"2026-05-18T00:11:19.433724+00:00"}