{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:Y47UP37KPS2LHNWOHDNZM74OCJ","short_pith_number":"pith:Y47UP37K","schema_version":"1.0","canonical_sha256":"c73f47efea7cb4b3b6ce38db967f8e1254692dce48896ac268b94f64031e760a","source":{"kind":"arxiv","id":"1803.10933","version":1},"attestation_state":"computed","paper":{"title":"Property (T) for locally compact groups and C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Bachir Bekka, Chi-Keung Ng","submitted_at":"2018-03-29T05:58:33Z","abstract_excerpt":"Let $G$ be a locally compact group and let $C^*(G)$ and $C^*_r(G)$ be the full group $C^*$-algebra and the reduced group $C^*$-algebra of $G$. We investigate the relationship between Property $(T)$ for $G$ and Property $(T)$ as well as its strong version for $C^*(G)$ and $C^*_r(G)$. We show that $G$ has Property $(T)$ if (and only if) $C^*(G)$ has Property $(T)$. In the case where $G$ is a locally compact IN-group, we prove that $G$ has Property $(T)$ if and only if $C^*_r(G)$ has strong Property $(T)$. We also show that $C^*_r(G)$ has strong Property $(T)$ for every non-amenable locally compa"},"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":"1803.10933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-03-29T05:58:33Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8135434eae3b284f30c5279f2f84625b8d4274977a4111aa2ff0b63e2777640b","abstract_canon_sha256":"1c442c2fb6fbae8fe1451e4efc453ab71b8151b2ed2105bf847a25527af79846"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:49.751384Z","signature_b64":"5WAIr/Gp70OEKYu6VnFpv+GOvfgvV5Xu6WTKqrzWZjiSWRILkkJ3h9DuXsOMKxfVHu3ISj52GzcRV89sb13tDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c73f47efea7cb4b3b6ce38db967f8e1254692dce48896ac268b94f64031e760a","last_reissued_at":"2026-05-18T00:19:49.750743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:49.750743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Property (T) for locally compact groups and C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Bachir Bekka, Chi-Keung Ng","submitted_at":"2018-03-29T05:58:33Z","abstract_excerpt":"Let $G$ be a locally compact group and let $C^*(G)$ and $C^*_r(G)$ be the full group $C^*$-algebra and the reduced group $C^*$-algebra of $G$. We investigate the relationship between Property $(T)$ for $G$ and Property $(T)$ as well as its strong version for $C^*(G)$ and $C^*_r(G)$. We show that $G$ has Property $(T)$ if (and only if) $C^*(G)$ has Property $(T)$. In the case where $G$ is a locally compact IN-group, we prove that $G$ has Property $(T)$ if and only if $C^*_r(G)$ has strong Property $(T)$. We also show that $C^*_r(G)$ has strong Property $(T)$ for every non-amenable locally compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10933","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":"1803.10933","created_at":"2026-05-18T00:19:49.750840+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10933v1","created_at":"2026-05-18T00:19:49.750840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10933","created_at":"2026-05-18T00:19:49.750840+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y47UP37KPS2L","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y47UP37KPS2LHNWO","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y47UP37K","created_at":"2026-05-18T12:33:04.347982+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/Y47UP37KPS2LHNWOHDNZM74OCJ","json":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ.json","graph_json":"https://pith.science/api/pith-number/Y47UP37KPS2LHNWOHDNZM74OCJ/graph.json","events_json":"https://pith.science/api/pith-number/Y47UP37KPS2LHNWOHDNZM74OCJ/events.json","paper":"https://pith.science/paper/Y47UP37K"},"agent_actions":{"view_html":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ","download_json":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ.json","view_paper":"https://pith.science/paper/Y47UP37K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10933&json=true","fetch_graph":"https://pith.science/api/pith-number/Y47UP37KPS2LHNWOHDNZM74OCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/Y47UP37KPS2LHNWOHDNZM74OCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ/action/storage_attestation","attest_author":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ/action/author_attestation","sign_citation":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ/action/citation_signature","submit_replication":"https://pith.science/pith/Y47UP37KPS2LHNWOHDNZM74OCJ/action/replication_record"}},"created_at":"2026-05-18T00:19:49.750840+00:00","updated_at":"2026-05-18T00:19:49.750840+00:00"}