{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ONUSEFB6UC2K63CGCYGBT2VA33","short_pith_number":"pith:ONUSEFB6","schema_version":"1.0","canonical_sha256":"736922143ea0b4af6c46160c19eaa0dec04e9d9ab44532af2d0d489664350c06","source":{"kind":"arxiv","id":"1106.6268","version":1},"attestation_state":"computed","paper":{"title":"Abelian Hermitian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.DG","authors_text":"Adrian Andrada, Isabel Dotti, Maria Laura Barberis","submitted_at":"2011-06-30T15:24:10Z","abstract_excerpt":"We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that such a Hermitian structure is K\\\"ahler if and only if the Lie group is the direct product of several copies of the real hyperbolic plane by a euclidean factor. Moreover, we show that if a left invariant Hermitian metric on a Lie group with an abelian complex structure has flat first canonical connection, then the Lie group is abelian."},"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":"1106.6268","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-30T15:24:10Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"b0344126e4767c57e546b917ea2010724912e387b1ad1b7728a0f55647518a1b","abstract_canon_sha256":"393bd88d8d140bbe57924ddc3f6376f91c6dcfa98b8a670ba66343a91b0a20b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:03.644281Z","signature_b64":"2AXyfy9Zof8aaKZUGJkSYDt63O5c4C+GnIC2xIYMBT3phOsI66j71HIuh3yk5Mg2Rd7XS02WmwPmfLvuavo1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"736922143ea0b4af6c46160c19eaa0dec04e9d9ab44532af2d0d489664350c06","last_reissued_at":"2026-05-18T04:19:03.643653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:03.643653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Abelian Hermitian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.DG","authors_text":"Adrian Andrada, Isabel Dotti, Maria Laura Barberis","submitted_at":"2011-06-30T15:24:10Z","abstract_excerpt":"We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that such a Hermitian structure is K\\\"ahler if and only if the Lie group is the direct product of several copies of the real hyperbolic plane by a euclidean factor. Moreover, we show that if a left invariant Hermitian metric on a Lie group with an abelian complex structure has flat first canonical connection, then the Lie group is abelian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6268","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":"1106.6268","created_at":"2026-05-18T04:19:03.643747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.6268v1","created_at":"2026-05-18T04:19:03.643747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6268","created_at":"2026-05-18T04:19:03.643747+00:00"},{"alias_kind":"pith_short_12","alias_value":"ONUSEFB6UC2K","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"ONUSEFB6UC2K63CG","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"ONUSEFB6","created_at":"2026-05-18T12:26:37.096874+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/ONUSEFB6UC2K63CGCYGBT2VA33","json":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33.json","graph_json":"https://pith.science/api/pith-number/ONUSEFB6UC2K63CGCYGBT2VA33/graph.json","events_json":"https://pith.science/api/pith-number/ONUSEFB6UC2K63CGCYGBT2VA33/events.json","paper":"https://pith.science/paper/ONUSEFB6"},"agent_actions":{"view_html":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33","download_json":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33.json","view_paper":"https://pith.science/paper/ONUSEFB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.6268&json=true","fetch_graph":"https://pith.science/api/pith-number/ONUSEFB6UC2K63CGCYGBT2VA33/graph.json","fetch_events":"https://pith.science/api/pith-number/ONUSEFB6UC2K63CGCYGBT2VA33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33/action/storage_attestation","attest_author":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33/action/author_attestation","sign_citation":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33/action/citation_signature","submit_replication":"https://pith.science/pith/ONUSEFB6UC2K63CGCYGBT2VA33/action/replication_record"}},"created_at":"2026-05-18T04:19:03.643747+00:00","updated_at":"2026-05-18T04:19:03.643747+00:00"}