{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GGP5F6MQOMNS3ZVC3EVE65SF5U","short_pith_number":"pith:GGP5F6MQ","schema_version":"1.0","canonical_sha256":"319fd2f990731b2de6a2d92a4f7645ed015f77e51350e4cb56cf9484c2d54b41","source":{"kind":"arxiv","id":"1502.05214","version":3},"attestation_state":"computed","paper":{"title":"Weak amenability of Fourier algebras and local synthesis of the anti-diagonal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Ebrahim Samei, Hun Hee Lee, Jean Ludwig, Nico Spronk","submitted_at":"2015-02-18T13:17:53Z","abstract_excerpt":"We show that for a connected Lie group $G$, its Fourier algebra $A(G)$ is weakly amenable only if $G$ is abelian. Our main new idea is to show that weak amenability of $A(G)$ implies that the anti-diagonal, $\\check{\\Delta}_G=\\{(g,g^{-1}):g\\in G\\}$, is a set of local synthesis for $A(G\\times G)$. We then show that this cannot happen if $G$ is non-abelian. We conclude for a locally compact group $G$, that $A(G)$ can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group $G$, $A(G)$ is weakly amenable if and only if its connected compo"},"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":"1502.05214","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-18T13:17:53Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"e3348c147910ff9ae2c21eca071ce2b46643e4329804b0fa7a808f707a9be60c","abstract_canon_sha256":"1ec9fb24a4160f26252024a8d666154bf8764eb6dca85450f855d4a61df09426"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:45.083804Z","signature_b64":"CTGZF3W2izuxZRxkoZ5pSLJP3HzmVLmtH2E2dGUXCgh1F1equV63bELbeLVZJ3QpvSkoTzrLlKBxYcQHWGFYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"319fd2f990731b2de6a2d92a4f7645ed015f77e51350e4cb56cf9484c2d54b41","last_reissued_at":"2026-05-18T01:21:45.082938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:45.082938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak amenability of Fourier algebras and local synthesis of the anti-diagonal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Ebrahim Samei, Hun Hee Lee, Jean Ludwig, Nico Spronk","submitted_at":"2015-02-18T13:17:53Z","abstract_excerpt":"We show that for a connected Lie group $G$, its Fourier algebra $A(G)$ is weakly amenable only if $G$ is abelian. Our main new idea is to show that weak amenability of $A(G)$ implies that the anti-diagonal, $\\check{\\Delta}_G=\\{(g,g^{-1}):g\\in G\\}$, is a set of local synthesis for $A(G\\times G)$. We then show that this cannot happen if $G$ is non-abelian. We conclude for a locally compact group $G$, that $A(G)$ can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group $G$, $A(G)$ is weakly amenable if and only if its connected compo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05214","kind":"arxiv","version":3},"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":"1502.05214","created_at":"2026-05-18T01:21:45.083090+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05214v3","created_at":"2026-05-18T01:21:45.083090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05214","created_at":"2026-05-18T01:21:45.083090+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGP5F6MQOMNS","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGP5F6MQOMNS3ZVC","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGP5F6MQ","created_at":"2026-05-18T12:29:22.688609+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/GGP5F6MQOMNS3ZVC3EVE65SF5U","json":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U.json","graph_json":"https://pith.science/api/pith-number/GGP5F6MQOMNS3ZVC3EVE65SF5U/graph.json","events_json":"https://pith.science/api/pith-number/GGP5F6MQOMNS3ZVC3EVE65SF5U/events.json","paper":"https://pith.science/paper/GGP5F6MQ"},"agent_actions":{"view_html":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U","download_json":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U.json","view_paper":"https://pith.science/paper/GGP5F6MQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05214&json=true","fetch_graph":"https://pith.science/api/pith-number/GGP5F6MQOMNS3ZVC3EVE65SF5U/graph.json","fetch_events":"https://pith.science/api/pith-number/GGP5F6MQOMNS3ZVC3EVE65SF5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U/action/storage_attestation","attest_author":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U/action/author_attestation","sign_citation":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U/action/citation_signature","submit_replication":"https://pith.science/pith/GGP5F6MQOMNS3ZVC3EVE65SF5U/action/replication_record"}},"created_at":"2026-05-18T01:21:45.083090+00:00","updated_at":"2026-05-18T01:21:45.083090+00:00"}