{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YWXXMBM2SCOMMQVFVK74OANG7G","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cb544181476cd622bd913ef7f00d9ca82310d731bf0492ed238f2d00ca130b2f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-28T09:05:35Z","title_canon_sha256":"bd4b3e2581225e67e1886b0d630f40d3a7dbdc00b65e01b6dc7a62fc8ace80a9"},"schema_version":"1.0","source":{"id":"1010.5896","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5896","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5896v2","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5896","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"YWXXMBM2SCOM","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YWXXMBM2SCOMMQVF","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YWXXMBM2","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:58627f19f9bc93d1555168dcd4678a62ff5fdea692200647bece45728e0f58a1","target":"graph","created_at":"2026-05-18T04:17:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The aim of this paper is to provide cohomologies of $n$-ary Hom-Nambu-Lie algebras governing central extensions and one parameter formal deformations. We generalize to $n$-ary algebras the notions of derivations and representation introduced by Sheng for Hom-Lie algebras. Also we show that a cohomology of $n$-ary Hom-Nambu-Lie algebras could be derived from the cohomology of Hom-Leibniz algebras.","authors_text":"A. Makhlouf, F. Ammar, S. Mabrouk","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-28T09:05:35Z","title":"Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5896","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:274b3edb2f5bfcc27dd6d49a0d4dfa7d1a1a4ab4e32c3a6235cf947128752c16","target":"record","created_at":"2026-05-18T04:17:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cb544181476cd622bd913ef7f00d9ca82310d731bf0492ed238f2d00ca130b2f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-10-28T09:05:35Z","title_canon_sha256":"bd4b3e2581225e67e1886b0d630f40d3a7dbdc00b65e01b6dc7a62fc8ace80a9"},"schema_version":"1.0","source":{"id":"1010.5896","kind":"arxiv","version":2}},"canonical_sha256":"c5af76059a909cc642a5aabfc701a6f9bfb47c21b0049439f0cca232b5e571e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5af76059a909cc642a5aabfc701a6f9bfb47c21b0049439f0cca232b5e571e5","first_computed_at":"2026-05-18T04:17:24.988568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:24.988568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"83JOGQyV28q9ahllrtC9utQF67am/yS184IuRipfPhCGX4cWu3zDHU5PcbVvtkXWi3Joop8FX1prtELGaBnSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:24.989169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:274b3edb2f5bfcc27dd6d49a0d4dfa7d1a1a4ab4e32c3a6235cf947128752c16","sha256:58627f19f9bc93d1555168dcd4678a62ff5fdea692200647bece45728e0f58a1"],"state_sha256":"ebe327ce4f0d645598b8008159ee235ebcc5b67dac9ce48a427f641a9b5e1470"}