{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PULSAWFQRFFSU2XO5JFEE7MP3N","short_pith_number":"pith:PULSAWFQ","schema_version":"1.0","canonical_sha256":"7d172058b0894b2a6aeeea4a427d8fdb6504195f0ceee09d70c2a26f08eec4ea","source":{"kind":"arxiv","id":"1709.08620","version":1},"attestation_state":"computed","paper":{"title":"Extensions of hom-Lie color algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"A. R. Armakan, M. R. Farhangdoost, S. Silvestrov","submitted_at":"2017-09-23T16:10:53Z","abstract_excerpt":"In this paper we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie algebra $\\mathfrak{g}$ by another hom-Lie algebra $\\mathfrak{h}$ and we discuss the case where $\\mathfrak{h}$ has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i"},"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":"1709.08620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-09-23T16:10:53Z","cross_cats_sorted":[],"title_canon_sha256":"342a004a38ff85436eb55700987c347b8a1a9b433e8f7f42cec5bae4b05f9713","abstract_canon_sha256":"1fec07d1aa55f0f29a96b0bdcb92537fd43ee497b4f24c8a0af1be7cb8f903d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:22.161522Z","signature_b64":"tIaKI+4WzCvL0wijPGHACqcHzkYL9DECuv6RYtvDEcxnN81HkMTfX/+40KZpMQX7mDE9dwb+btb5hl65DWjKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d172058b0894b2a6aeeea4a427d8fdb6504195f0ceee09d70c2a26f08eec4ea","last_reissued_at":"2026-05-18T00:34:22.160954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:22.160954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensions of hom-Lie color algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"A. R. Armakan, M. R. Farhangdoost, S. Silvestrov","submitted_at":"2017-09-23T16:10:53Z","abstract_excerpt":"In this paper we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie algebra $\\mathfrak{g}$ by another hom-Lie algebra $\\mathfrak{h}$ and we discuss the case where $\\mathfrak{h}$ has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08620","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":"1709.08620","created_at":"2026-05-18T00:34:22.161042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.08620v1","created_at":"2026-05-18T00:34:22.161042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08620","created_at":"2026-05-18T00:34:22.161042+00:00"},{"alias_kind":"pith_short_12","alias_value":"PULSAWFQRFFS","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PULSAWFQRFFSU2XO","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PULSAWFQ","created_at":"2026-05-18T12:31:37.085036+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/PULSAWFQRFFSU2XO5JFEE7MP3N","json":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N.json","graph_json":"https://pith.science/api/pith-number/PULSAWFQRFFSU2XO5JFEE7MP3N/graph.json","events_json":"https://pith.science/api/pith-number/PULSAWFQRFFSU2XO5JFEE7MP3N/events.json","paper":"https://pith.science/paper/PULSAWFQ"},"agent_actions":{"view_html":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N","download_json":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N.json","view_paper":"https://pith.science/paper/PULSAWFQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.08620&json=true","fetch_graph":"https://pith.science/api/pith-number/PULSAWFQRFFSU2XO5JFEE7MP3N/graph.json","fetch_events":"https://pith.science/api/pith-number/PULSAWFQRFFSU2XO5JFEE7MP3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N/action/storage_attestation","attest_author":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N/action/author_attestation","sign_citation":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N/action/citation_signature","submit_replication":"https://pith.science/pith/PULSAWFQRFFSU2XO5JFEE7MP3N/action/replication_record"}},"created_at":"2026-05-18T00:34:22.161042+00:00","updated_at":"2026-05-18T00:34:22.161042+00:00"}