{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7M3MUMXVTI35QSLLNAT54X23B2","short_pith_number":"pith:7M3MUMXV","schema_version":"1.0","canonical_sha256":"fb36ca32f59a37d8496b6827de5f5b0e98d46fc0bf474d7bcfe35e2f0c24dcb3","source":{"kind":"arxiv","id":"1410.2339","version":5},"attestation_state":"computed","paper":{"title":"A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have $\\mathbb{Q}$-Forms","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dave Witte Morris","submitted_at":"2014-10-09T02:57:26Z","abstract_excerpt":"A Lie algebra $\\mathfrak{g}_\\mathbb{Q}$ over $\\mathbb{Q}$ is said to be $\\mathbb{R}$-universal if every homomorphism from $\\mathfrak{g}_\\mathbb{Q}$ to $\\mathfrak{gl}(n,\\mathbb{R})$ is conjugate to a homomorphism into $\\mathfrak{gl}(n,\\mathbb{Q})$ (for every $n$). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an $\\mathbb{R}$-universal $\\mathbb{Q}$-form. We also provide a classification of the $\\mathbb{R}$-universal Lie algebras that are semisimple."},"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":"1410.2339","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RT","submitted_at":"2014-10-09T02:57:26Z","cross_cats_sorted":[],"title_canon_sha256":"218b5a442fe967b269194ca4d6724bf2550f559a9a7843a381b3e5a8f3840fe3","abstract_canon_sha256":"8e768d3270d9d29706164a71a5b20abc43bd138af84fc7c3b3894ade77909a13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:51.806870Z","signature_b64":"n8OMnitET2dLJf0IMzjir2kiBt0USrOpDHuTyDGJS9rngE0lv963TS7ngKYD1l83TMG2WHNIMFKKr0LbaytnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb36ca32f59a37d8496b6827de5f5b0e98d46fc0bf474d7bcfe35e2f0c24dcb3","last_reissued_at":"2026-05-18T02:17:51.806109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:51.806109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have $\\mathbb{Q}$-Forms","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dave Witte Morris","submitted_at":"2014-10-09T02:57:26Z","abstract_excerpt":"A Lie algebra $\\mathfrak{g}_\\mathbb{Q}$ over $\\mathbb{Q}$ is said to be $\\mathbb{R}$-universal if every homomorphism from $\\mathfrak{g}_\\mathbb{Q}$ to $\\mathfrak{gl}(n,\\mathbb{R})$ is conjugate to a homomorphism into $\\mathfrak{gl}(n,\\mathbb{Q})$ (for every $n$). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an $\\mathbb{R}$-universal $\\mathbb{Q}$-form. We also provide a classification of the $\\mathbb{R}$-universal Lie algebras that are semisimple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2339","kind":"arxiv","version":5},"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":"1410.2339","created_at":"2026-05-18T02:17:51.806228+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2339v5","created_at":"2026-05-18T02:17:51.806228+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2339","created_at":"2026-05-18T02:17:51.806228+00:00"},{"alias_kind":"pith_short_12","alias_value":"7M3MUMXVTI35","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7M3MUMXVTI35QSLL","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7M3MUMXV","created_at":"2026-05-18T12:28:19.803747+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/7M3MUMXVTI35QSLLNAT54X23B2","json":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2.json","graph_json":"https://pith.science/api/pith-number/7M3MUMXVTI35QSLLNAT54X23B2/graph.json","events_json":"https://pith.science/api/pith-number/7M3MUMXVTI35QSLLNAT54X23B2/events.json","paper":"https://pith.science/paper/7M3MUMXV"},"agent_actions":{"view_html":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2","download_json":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2.json","view_paper":"https://pith.science/paper/7M3MUMXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2339&json=true","fetch_graph":"https://pith.science/api/pith-number/7M3MUMXVTI35QSLLNAT54X23B2/graph.json","fetch_events":"https://pith.science/api/pith-number/7M3MUMXVTI35QSLLNAT54X23B2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2/action/storage_attestation","attest_author":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2/action/author_attestation","sign_citation":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2/action/citation_signature","submit_replication":"https://pith.science/pith/7M3MUMXVTI35QSLLNAT54X23B2/action/replication_record"}},"created_at":"2026-05-18T02:17:51.806228+00:00","updated_at":"2026-05-18T02:17:51.806228+00:00"}