{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VLRLMGAMMI2EGI6SD4CMYNWGOG","short_pith_number":"pith:VLRLMGAM","schema_version":"1.0","canonical_sha256":"aae2b6180c62344323d21f04cc36c671a3b0ccd2636ad87ee2af28b9abe0841a","source":{"kind":"arxiv","id":"1607.04869","version":3},"attestation_state":"computed","paper":{"title":"A quantum version of the algebra of distributions of $\\operatorname{SL}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Iv\\'an Angiono","submitted_at":"2016-07-17T13:33:19Z","abstract_excerpt":"Let $\\lambda$ be a primitive root of unity of order $\\ell$. We introduce a family of finite-dimensional algebras $\\{\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)\\}_{N\\in\\mathbb{N}_0}$ over the complex numbers, such that $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a subalgebra of $\\mathcal{D}_{\\lambda,M}(\\mathfrak{sl}_2)$ if $N<M$, and $\\mathcal{D}_{\\lambda,N-1}(\\mathfrak{sl}_2)\\subset \\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a $\\mathfrak{u}_{\\lambda}(\\mathfrak{sl}_2)$-cleft extension.\n  The simple $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$-modules $(\\mathcal{L}_{N}(p))_{0\\le p<\\ell^{N+1}}$ ar"},"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":"1607.04869","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-17T13:33:19Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"4e3b9d1957e91f0d75eb7d3289efd6506d7d135db28c7872dc0193cff9f410d5","abstract_canon_sha256":"94d54a0ac52e1ef84290fc780428a31ae555cbf93775bea0334c2f4c2e07c68e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:39.659828Z","signature_b64":"mL253Hfwk1pQKG55uYJzmxFo+GVxaLw+ZCGZo14x9mHL6WpnUsH9M3xukftto047W5G6jh+zUbUPGxhH7DS6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aae2b6180c62344323d21f04cc36c671a3b0ccd2636ad87ee2af28b9abe0841a","last_reissued_at":"2026-05-18T00:43:39.659360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:39.659360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A quantum version of the algebra of distributions of $\\operatorname{SL}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Iv\\'an Angiono","submitted_at":"2016-07-17T13:33:19Z","abstract_excerpt":"Let $\\lambda$ be a primitive root of unity of order $\\ell$. We introduce a family of finite-dimensional algebras $\\{\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)\\}_{N\\in\\mathbb{N}_0}$ over the complex numbers, such that $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a subalgebra of $\\mathcal{D}_{\\lambda,M}(\\mathfrak{sl}_2)$ if $N<M$, and $\\mathcal{D}_{\\lambda,N-1}(\\mathfrak{sl}_2)\\subset \\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a $\\mathfrak{u}_{\\lambda}(\\mathfrak{sl}_2)$-cleft extension.\n  The simple $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$-modules $(\\mathcal{L}_{N}(p))_{0\\le p<\\ell^{N+1}}$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04869","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":"1607.04869","created_at":"2026-05-18T00:43:39.659426+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.04869v3","created_at":"2026-05-18T00:43:39.659426+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04869","created_at":"2026-05-18T00:43:39.659426+00:00"},{"alias_kind":"pith_short_12","alias_value":"VLRLMGAMMI2E","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VLRLMGAMMI2EGI6S","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VLRLMGAM","created_at":"2026-05-18T12:30:48.956258+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/VLRLMGAMMI2EGI6SD4CMYNWGOG","json":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG.json","graph_json":"https://pith.science/api/pith-number/VLRLMGAMMI2EGI6SD4CMYNWGOG/graph.json","events_json":"https://pith.science/api/pith-number/VLRLMGAMMI2EGI6SD4CMYNWGOG/events.json","paper":"https://pith.science/paper/VLRLMGAM"},"agent_actions":{"view_html":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG","download_json":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG.json","view_paper":"https://pith.science/paper/VLRLMGAM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.04869&json=true","fetch_graph":"https://pith.science/api/pith-number/VLRLMGAMMI2EGI6SD4CMYNWGOG/graph.json","fetch_events":"https://pith.science/api/pith-number/VLRLMGAMMI2EGI6SD4CMYNWGOG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/action/storage_attestation","attest_author":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/action/author_attestation","sign_citation":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/action/citation_signature","submit_replication":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/action/replication_record"}},"created_at":"2026-05-18T00:43:39.659426+00:00","updated_at":"2026-05-18T00:43:39.659426+00:00"}