{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AI2G2S3CGKLSUXFH4ZG5XDQURW","short_pith_number":"pith:AI2G2S3C","schema_version":"1.0","canonical_sha256":"02346d4b6232972a5ca7e64ddb8e148d874e15488b9d64f8c5b0e0f76274fc15","source":{"kind":"arxiv","id":"1703.07148","version":1},"attestation_state":"computed","paper":{"title":"The Schur Lie-Multiplier of Leibinz Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"J. M. Casas, M. A. Insua","submitted_at":"2017-03-21T11:08:59Z","abstract_excerpt":"For a free presentation $0 \\to R \\to F \\to G \\to 0$ of a Leibniz algebra $G$, the Baer invariant ${\\cal M}^{\\sf Lie}(G) = \\frac{R \\cap [F, F]_{Lie}}{[F, R]_{Lie}}$ is called the Schur multiplier of $G$ relative to the Liezation functor or Schur Lie-multiplier. For a two-sided ideal $N$ of a Leibniz algebra $G$, we construct a four-term exact sequence relating the Schur Lie-multiplier of $G$ and $G/N$, which is applied to study and characterize Lie-nilpotency, Lie-stem covers and Lie-capability of Leibniz algebras."},"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":"1703.07148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-03-21T11:08:59Z","cross_cats_sorted":[],"title_canon_sha256":"2454b97b5c5ddcb03316038cbb431b8f0a300c96a7064f362c66e6a36324c265","abstract_canon_sha256":"90ef70179680df00233609e06880ac34cccf1d5b1f6f4835a09867152ee7a300"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:11.191422Z","signature_b64":"wS8MUZkWyOeBIPVWi0jFTG0td3nTr9N7Hx6MLae5Ji8W1PzalQAltu03PgOIUJXahcxTAwE0u87KfiMXMj/pBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02346d4b6232972a5ca7e64ddb8e148d874e15488b9d64f8c5b0e0f76274fc15","last_reissued_at":"2026-05-18T00:48:11.190844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:11.190844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Schur Lie-Multiplier of Leibinz Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"J. M. Casas, M. A. Insua","submitted_at":"2017-03-21T11:08:59Z","abstract_excerpt":"For a free presentation $0 \\to R \\to F \\to G \\to 0$ of a Leibniz algebra $G$, the Baer invariant ${\\cal M}^{\\sf Lie}(G) = \\frac{R \\cap [F, F]_{Lie}}{[F, R]_{Lie}}$ is called the Schur multiplier of $G$ relative to the Liezation functor or Schur Lie-multiplier. For a two-sided ideal $N$ of a Leibniz algebra $G$, we construct a four-term exact sequence relating the Schur Lie-multiplier of $G$ and $G/N$, which is applied to study and characterize Lie-nilpotency, Lie-stem covers and Lie-capability of Leibniz algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07148","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":"1703.07148","created_at":"2026-05-18T00:48:11.190929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.07148v1","created_at":"2026-05-18T00:48:11.190929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07148","created_at":"2026-05-18T00:48:11.190929+00:00"},{"alias_kind":"pith_short_12","alias_value":"AI2G2S3CGKLS","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AI2G2S3CGKLSUXFH","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AI2G2S3C","created_at":"2026-05-18T12:31:05.417338+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/AI2G2S3CGKLSUXFH4ZG5XDQURW","json":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW.json","graph_json":"https://pith.science/api/pith-number/AI2G2S3CGKLSUXFH4ZG5XDQURW/graph.json","events_json":"https://pith.science/api/pith-number/AI2G2S3CGKLSUXFH4ZG5XDQURW/events.json","paper":"https://pith.science/paper/AI2G2S3C"},"agent_actions":{"view_html":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW","download_json":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW.json","view_paper":"https://pith.science/paper/AI2G2S3C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.07148&json=true","fetch_graph":"https://pith.science/api/pith-number/AI2G2S3CGKLSUXFH4ZG5XDQURW/graph.json","fetch_events":"https://pith.science/api/pith-number/AI2G2S3CGKLSUXFH4ZG5XDQURW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW/action/storage_attestation","attest_author":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW/action/author_attestation","sign_citation":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW/action/citation_signature","submit_replication":"https://pith.science/pith/AI2G2S3CGKLSUXFH4ZG5XDQURW/action/replication_record"}},"created_at":"2026-05-18T00:48:11.190929+00:00","updated_at":"2026-05-18T00:48:11.190929+00:00"}