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The relations assert that \\begin{equation*} [A,B]=[B,C]=[C,A]=2D \\end{equation*} and each of the elements \\begin{gather*} \\alpha=[A,D]+AC-BA, \\qquad \\beta=[B,D]+BA-CB, \\qquad \\gamma=[C,D]+CB-AC \\end{gather*} is central in $\\Re$. Additionally the element $\\delta=A+B+C$ is central in $\\Re$.\n  In this paper we explore the relationship between the Racah algebra $\\R"},"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":"1907.02135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-03T21:12:48Z","cross_cats_sorted":[],"title_canon_sha256":"c097ae13b11868df5e9bc92fdb21574ff8a14e9d6bb98e71373cfba743782176","abstract_canon_sha256":"617b14cb417bdbe23474665589400695b08e4e3f178ce413431dc656b45fae8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:29.755468Z","signature_b64":"7Q519xHGBKAmQWu45KqIT/imSkKNEzZQIDdcp1EwfizDh/DOkPgQH9QO0YES9cEG83sjnWLGaH5VNZGjqLUFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59de3d9d2ce1bd8cb251de1eec9bf942168985a624d11c54ea5d094130ead673","last_reissued_at":"2026-05-17T23:41:29.754741Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:29.754741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The universal enveloping algebra of $\\mathfrak{sl}_2$ and the Racah algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Hau-wen Huang, Sarah Bockting-Conrad","submitted_at":"2019-07-03T21:12:48Z","abstract_excerpt":"Let $\\mathbb{F}$ denote a field with ${\\rm char\\,}\\mathbb{F}\\not=2$. The Racah algebra $\\Re$ is the unital associative $\\mathbb{F}$-algebra defined by generators and relations in the following way. The generators are $A$, $B$, $C$, $D$. The relations assert that \\begin{equation*} [A,B]=[B,C]=[C,A]=2D \\end{equation*} and each of the elements \\begin{gather*} \\alpha=[A,D]+AC-BA, \\qquad \\beta=[B,D]+BA-CB, \\qquad \\gamma=[C,D]+CB-AC \\end{gather*} is central in $\\Re$. Additionally the element $\\delta=A+B+C$ is central in $\\Re$.\n  In this paper we explore the relationship between the Racah algebra $\\R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02135","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":"1907.02135","created_at":"2026-05-17T23:41:29.754861+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02135v1","created_at":"2026-05-17T23:41:29.754861+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02135","created_at":"2026-05-17T23:41:29.754861+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHPD3HJM4G6Y","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHPD3HJM4G6YZMSR","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHPD3HJM","created_at":"2026-05-18T12:33:21.387695+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/LHPD3HJM4G6YZMSR3YPOZG7ZII","json":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII.json","graph_json":"https://pith.science/api/pith-number/LHPD3HJM4G6YZMSR3YPOZG7ZII/graph.json","events_json":"https://pith.science/api/pith-number/LHPD3HJM4G6YZMSR3YPOZG7ZII/events.json","paper":"https://pith.science/paper/LHPD3HJM"},"agent_actions":{"view_html":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII","download_json":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII.json","view_paper":"https://pith.science/paper/LHPD3HJM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02135&json=true","fetch_graph":"https://pith.science/api/pith-number/LHPD3HJM4G6YZMSR3YPOZG7ZII/graph.json","fetch_events":"https://pith.science/api/pith-number/LHPD3HJM4G6YZMSR3YPOZG7ZII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII/action/storage_attestation","attest_author":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII/action/author_attestation","sign_citation":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII/action/citation_signature","submit_replication":"https://pith.science/pith/LHPD3HJM4G6YZMSR3YPOZG7ZII/action/replication_record"}},"created_at":"2026-05-17T23:41:29.754861+00:00","updated_at":"2026-05-17T23:41:29.754861+00:00"}