{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:IG3KCTQVRSIPKOQRS7JFISOFKX","short_pith_number":"pith:IG3KCTQV","schema_version":"1.0","canonical_sha256":"41b6a14e158c90f53a1197d25449c555cfee59d8d163082d00de20342bde5794","source":{"kind":"arxiv","id":"0902.3348","version":1},"attestation_state":"computed","paper":{"title":"On Lie algebras associated with representation directed algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Justyna Kosakowska, Stanis{\\l}aw Kasjan","submitted_at":"2009-02-19T11:31:42Z","abstract_excerpt":"Let $B$ be a representation-finite $\\mathbb{C}$-algebra.\n  The $\\mathbb{Z}$-Lie algebra $L(B)$ associated with $B$ has been defined by Ch. Riedtmann.\n  If $B$ is representation-directed there is another $\\mathbb{Z}$-Lie algebra associated with $B$ defined by C. M. Ringel and denoted by $\\CK(B)$. We prove that the Lie algebras $L(B)$ and $\\CK(B)$ are isomorphic for any representation-directed $\\mathbb{C}$-algebra $B$."},"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":"0902.3348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-02-19T11:31:42Z","cross_cats_sorted":[],"title_canon_sha256":"0e3e10fb6dde23abb3ce01a8121f1fe17e5146d064ff88bd0599dbe116963511","abstract_canon_sha256":"d75ed6f51a84683e66d867532e643a519b9cfa2d415473b8d64ff0a50ff5ddc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:06.924647Z","signature_b64":"bqexsszviNWTSUIw7DLHKZsRCmIh0al2APkebnB5hc2NVtgBsYhOmKW7PI+f5a3fpiUuDVCmq/uSnTL9ngSBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41b6a14e158c90f53a1197d25449c555cfee59d8d163082d00de20342bde5794","last_reissued_at":"2026-05-18T03:20:06.923978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:06.923978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Lie algebras associated with representation directed algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Justyna Kosakowska, Stanis{\\l}aw Kasjan","submitted_at":"2009-02-19T11:31:42Z","abstract_excerpt":"Let $B$ be a representation-finite $\\mathbb{C}$-algebra.\n  The $\\mathbb{Z}$-Lie algebra $L(B)$ associated with $B$ has been defined by Ch. Riedtmann.\n  If $B$ is representation-directed there is another $\\mathbb{Z}$-Lie algebra associated with $B$ defined by C. M. Ringel and denoted by $\\CK(B)$. We prove that the Lie algebras $L(B)$ and $\\CK(B)$ are isomorphic for any representation-directed $\\mathbb{C}$-algebra $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3348","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":"0902.3348","created_at":"2026-05-18T03:20:06.924085+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.3348v1","created_at":"2026-05-18T03:20:06.924085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.3348","created_at":"2026-05-18T03:20:06.924085+00:00"},{"alias_kind":"pith_short_12","alias_value":"IG3KCTQVRSIP","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"IG3KCTQVRSIPKOQR","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"IG3KCTQV","created_at":"2026-05-18T12:26:00.592388+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/IG3KCTQVRSIPKOQRS7JFISOFKX","json":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX.json","graph_json":"https://pith.science/api/pith-number/IG3KCTQVRSIPKOQRS7JFISOFKX/graph.json","events_json":"https://pith.science/api/pith-number/IG3KCTQVRSIPKOQRS7JFISOFKX/events.json","paper":"https://pith.science/paper/IG3KCTQV"},"agent_actions":{"view_html":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX","download_json":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX.json","view_paper":"https://pith.science/paper/IG3KCTQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.3348&json=true","fetch_graph":"https://pith.science/api/pith-number/IG3KCTQVRSIPKOQRS7JFISOFKX/graph.json","fetch_events":"https://pith.science/api/pith-number/IG3KCTQVRSIPKOQRS7JFISOFKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX/action/storage_attestation","attest_author":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX/action/author_attestation","sign_citation":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX/action/citation_signature","submit_replication":"https://pith.science/pith/IG3KCTQVRSIPKOQRS7JFISOFKX/action/replication_record"}},"created_at":"2026-05-18T03:20:06.924085+00:00","updated_at":"2026-05-18T03:20:06.924085+00:00"}