{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SOA7LIGVLNYNBDIIJW57FCB2H4","short_pith_number":"pith:SOA7LIGV","schema_version":"1.0","canonical_sha256":"9381f5a0d55b70d08d084dbbf2883a3f2d18e56cac0c6d4afa9ad1d17f68a457","source":{"kind":"arxiv","id":"1710.10173","version":1},"attestation_state":"computed","paper":{"title":"The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"G. R. Biyogmam, J. M. Casas","submitted_at":"2017-10-26T16:49:53Z","abstract_excerpt":"We introduce the notion of c-nilpotent Schur Lie-multiplier of Leibniz algebras. We obtain exact sequences and formulas of the dimensions of the underlying vector spaces relating the c-nilpotent Schur Lie-multiplier of a Leibniz algebra Q and its quotient by a two-sided ideal. These tools are used to characterize Lie-nilpotency and c-Lie-stem covers of Leibniz algebras. We prove the existence of c-Lie-stem covers for finite dimensional Leibniz algebras and the non existence of c-covering on certain Lie-nilpotent Leibniz algebras with non trivial c-nilpotent Schur Lie-multiplier, and we provide"},"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":"1710.10173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-10-26T16:49:53Z","cross_cats_sorted":[],"title_canon_sha256":"3131e9577fa3b506ec13c679e7a7c5d633f94d300c029dac0a73764e54957847","abstract_canon_sha256":"e12e6679140682acdd9f295598a6577cd013b3dcaa8ca21e3df0b7a6eada78a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:54.609845Z","signature_b64":"gtd6OLtsBYJaIe8Uxx5m2DmpQbwE3Wzjj129KKKjLYpI38Kf3Avh47LsX5iMRtjoCP/roAodMcdvC6XeA032Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9381f5a0d55b70d08d084dbbf2883a3f2d18e56cac0c6d4afa9ad1d17f68a457","last_reissued_at":"2026-05-18T00:31:54.609184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:54.609184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"G. R. Biyogmam, J. M. Casas","submitted_at":"2017-10-26T16:49:53Z","abstract_excerpt":"We introduce the notion of c-nilpotent Schur Lie-multiplier of Leibniz algebras. We obtain exact sequences and formulas of the dimensions of the underlying vector spaces relating the c-nilpotent Schur Lie-multiplier of a Leibniz algebra Q and its quotient by a two-sided ideal. These tools are used to characterize Lie-nilpotency and c-Lie-stem covers of Leibniz algebras. We prove the existence of c-Lie-stem covers for finite dimensional Leibniz algebras and the non existence of c-covering on certain Lie-nilpotent Leibniz algebras with non trivial c-nilpotent Schur Lie-multiplier, and we provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10173","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":"1710.10173","created_at":"2026-05-18T00:31:54.609280+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10173v1","created_at":"2026-05-18T00:31:54.609280+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10173","created_at":"2026-05-18T00:31:54.609280+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOA7LIGVLNYN","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOA7LIGVLNYNBDII","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOA7LIGV","created_at":"2026-05-18T12:31:43.269735+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/SOA7LIGVLNYNBDIIJW57FCB2H4","json":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4.json","graph_json":"https://pith.science/api/pith-number/SOA7LIGVLNYNBDIIJW57FCB2H4/graph.json","events_json":"https://pith.science/api/pith-number/SOA7LIGVLNYNBDIIJW57FCB2H4/events.json","paper":"https://pith.science/paper/SOA7LIGV"},"agent_actions":{"view_html":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4","download_json":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4.json","view_paper":"https://pith.science/paper/SOA7LIGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10173&json=true","fetch_graph":"https://pith.science/api/pith-number/SOA7LIGVLNYNBDIIJW57FCB2H4/graph.json","fetch_events":"https://pith.science/api/pith-number/SOA7LIGVLNYNBDIIJW57FCB2H4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4/action/storage_attestation","attest_author":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4/action/author_attestation","sign_citation":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4/action/citation_signature","submit_replication":"https://pith.science/pith/SOA7LIGVLNYNBDIIJW57FCB2H4/action/replication_record"}},"created_at":"2026-05-18T00:31:54.609280+00:00","updated_at":"2026-05-18T00:31:54.609280+00:00"}