{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:TGEHQAWATHFATBSNLOEPPXYRNX","short_pith_number":"pith:TGEHQAWA","schema_version":"1.0","canonical_sha256":"99887802c099ca09864d5b88f7df116dcf09335f52e73516b6bee63da4b8522a","source":{"kind":"arxiv","id":"2307.09102","version":2},"attestation_state":"computed","paper":{"title":"Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alfonso Di Bartolo, Gianmarco La Rosa, Manuel Mancini","submitted_at":"2023-07-18T09:51:27Z","abstract_excerpt":"In this paper we study non-nilpotent non-Lie Leibniz $\\mathbb{F}$-algebras with one-dimensional derived subalgebra, where $\\mathbb{F}$ is a field with $\\operatorname{char}(\\mathbb{F}) \\neq 2$. We prove that such an algebra is isomorphic to the direct sum of the two-dimensional non-nilpotent non-Lie Leibniz algebra and an abelian algebra. We denote it by $L_n$, where $n=\\dim_{\\mathbb{F}} L_n$. This generalizes the result found in [11], which is only valid when $\\mathbb{F}=\\mathbb{C}$. Moreover, we find the Lie algebra of derivations, its Lie group of automorphisms and the Leibniz algebra of bid"},"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":"2307.09102","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2023-07-18T09:51:27Z","cross_cats_sorted":[],"title_canon_sha256":"5bc00a8f450cc3ca428d3dd88e4e36a71b5fea990187fe263ad1260c3591e9d5","abstract_canon_sha256":"be4b564ea815b1b6d0ec286fac1fc3d9557e9f415efc7a135da24c897a34a236"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:45.082081Z","signature_b64":"WISE10DCSgMq3TX8g54yshigdI6DRvTTLpy/qnAtGrUtbDQdUwUiDBGIrkAuOV4h+a2PXR2pnZ4CdlbLYuFwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99887802c099ca09864d5b88f7df116dcf09335f52e73516b6bee63da4b8522a","last_reissued_at":"2026-05-20T00:02:45.081477Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:45.081477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alfonso Di Bartolo, Gianmarco La Rosa, Manuel Mancini","submitted_at":"2023-07-18T09:51:27Z","abstract_excerpt":"In this paper we study non-nilpotent non-Lie Leibniz $\\mathbb{F}$-algebras with one-dimensional derived subalgebra, where $\\mathbb{F}$ is a field with $\\operatorname{char}(\\mathbb{F}) \\neq 2$. We prove that such an algebra is isomorphic to the direct sum of the two-dimensional non-nilpotent non-Lie Leibniz algebra and an abelian algebra. We denote it by $L_n$, where $n=\\dim_{\\mathbb{F}} L_n$. This generalizes the result found in [11], which is only valid when $\\mathbb{F}=\\mathbb{C}$. Moreover, we find the Lie algebra of derivations, its Lie group of automorphisms and the Leibniz algebra of bid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.09102","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.09102/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2307.09102","created_at":"2026-05-20T00:02:45.081555+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.09102v2","created_at":"2026-05-20T00:02:45.081555+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.09102","created_at":"2026-05-20T00:02:45.081555+00:00"},{"alias_kind":"pith_short_12","alias_value":"TGEHQAWATHFA","created_at":"2026-05-20T00:02:45.081555+00:00"},{"alias_kind":"pith_short_16","alias_value":"TGEHQAWATHFATBSN","created_at":"2026-05-20T00:02:45.081555+00:00"},{"alias_kind":"pith_short_8","alias_value":"TGEHQAWA","created_at":"2026-05-20T00:02:45.081555+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/TGEHQAWATHFATBSNLOEPPXYRNX","json":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX.json","graph_json":"https://pith.science/api/pith-number/TGEHQAWATHFATBSNLOEPPXYRNX/graph.json","events_json":"https://pith.science/api/pith-number/TGEHQAWATHFATBSNLOEPPXYRNX/events.json","paper":"https://pith.science/paper/TGEHQAWA"},"agent_actions":{"view_html":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX","download_json":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX.json","view_paper":"https://pith.science/paper/TGEHQAWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.09102&json=true","fetch_graph":"https://pith.science/api/pith-number/TGEHQAWATHFATBSNLOEPPXYRNX/graph.json","fetch_events":"https://pith.science/api/pith-number/TGEHQAWATHFATBSNLOEPPXYRNX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX/action/storage_attestation","attest_author":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX/action/author_attestation","sign_citation":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX/action/citation_signature","submit_replication":"https://pith.science/pith/TGEHQAWATHFATBSNLOEPPXYRNX/action/replication_record"}},"created_at":"2026-05-20T00:02:45.081555+00:00","updated_at":"2026-05-20T00:02:45.081555+00:00"}