{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:DEIQDHC4KKO5YDDJAR64E5RK37","short_pith_number":"pith:DEIQDHC4","schema_version":"1.0","canonical_sha256":"1911019c5c529ddc0c69047dc2762adfc95168ce3f3cc677c4323ad4c1c6ad27","source":{"kind":"arxiv","id":"1005.0456","version":1},"attestation_state":"computed","paper":{"title":"Cohomology and Deformations of Hom-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.RA","authors_text":"Abdenacer Makhlouf, Faouzi Ammar, Zeyneb Ejbehi","submitted_at":"2010-05-04T07:42:53Z","abstract_excerpt":"The purpose of this paper is to define  cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were  introduced by Makhlouf and Silvestrov in the study of one-parameter formal  deformations theory. Among  the relevant formulas for a generalization of Hochschild cohomology for Hom-associative algebras and  a Chevalley-Eilenberg cohomology for  Hom-Lie algebras, we define  Gerstenhaber bracket on the space of multilinear mappings of Hom-associative algebras and  Nijenhuis-Richardson bracket on the space of multilinear mappings of Hom-Lie alge"},"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":"1005.0456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-05-04T07:42:53Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"2840a42d045413f7ce1b7e07b0bfd510fc555d0b535d762c8488cd644d424a71","abstract_canon_sha256":"63eec42cbba2582e81f8ab04fdc9e0b6534c2b5572ccbd6cde18dded37a91470"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:09.146268Z","signature_b64":"iQJ6VLgjjMe/mRgmCfPuEy9G4Yu1rKtV9Kv/eCquZSNh917mJ0VCZVT3nhKmGuihhDFLz5W73vJFw8V7WbewAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1911019c5c529ddc0c69047dc2762adfc95168ce3f3cc677c4323ad4c1c6ad27","last_reissued_at":"2026-05-18T02:24:09.145793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:09.145793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology and Deformations of Hom-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.RA","authors_text":"Abdenacer Makhlouf, Faouzi Ammar, Zeyneb Ejbehi","submitted_at":"2010-05-04T07:42:53Z","abstract_excerpt":"The purpose of this paper is to define  cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were  introduced by Makhlouf and Silvestrov in the study of one-parameter formal  deformations theory. Among  the relevant formulas for a generalization of Hochschild cohomology for Hom-associative algebras and  a Chevalley-Eilenberg cohomology for  Hom-Lie algebras, we define  Gerstenhaber bracket on the space of multilinear mappings of Hom-associative algebras and  Nijenhuis-Richardson bracket on the space of multilinear mappings of Hom-Lie alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0456","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":"1005.0456","created_at":"2026-05-18T02:24:09.145863+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.0456v1","created_at":"2026-05-18T02:24:09.145863+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0456","created_at":"2026-05-18T02:24:09.145863+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEIQDHC4KKO5","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEIQDHC4KKO5YDDJ","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEIQDHC4","created_at":"2026-05-18T12:26:06.534383+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/DEIQDHC4KKO5YDDJAR64E5RK37","json":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37.json","graph_json":"https://pith.science/api/pith-number/DEIQDHC4KKO5YDDJAR64E5RK37/graph.json","events_json":"https://pith.science/api/pith-number/DEIQDHC4KKO5YDDJAR64E5RK37/events.json","paper":"https://pith.science/paper/DEIQDHC4"},"agent_actions":{"view_html":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37","download_json":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37.json","view_paper":"https://pith.science/paper/DEIQDHC4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.0456&json=true","fetch_graph":"https://pith.science/api/pith-number/DEIQDHC4KKO5YDDJAR64E5RK37/graph.json","fetch_events":"https://pith.science/api/pith-number/DEIQDHC4KKO5YDDJAR64E5RK37/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37/action/storage_attestation","attest_author":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37/action/author_attestation","sign_citation":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37/action/citation_signature","submit_replication":"https://pith.science/pith/DEIQDHC4KKO5YDDJAR64E5RK37/action/replication_record"}},"created_at":"2026-05-18T02:24:09.145863+00:00","updated_at":"2026-05-18T02:24:09.145863+00:00"}