{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:P23OXEKKEHE7PIC4IVONA2GZLJ","short_pith_number":"pith:P23OXEKK","schema_version":"1.0","canonical_sha256":"7eb6eb914a21c9f7a05c455cd068d95a7f9cf84f2fa803ea76121b0dbd673e10","source":{"kind":"arxiv","id":"1908.06928","version":2},"attestation_state":"computed","paper":{"title":"Character rigidity of simple algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Bachir Bekka","submitted_at":"2019-08-19T16:56:58Z","abstract_excerpt":"We prove the following extension of Tits' simplicity theorem. Let $k$ be an infinite field, $G$ an algebraic group defined and quasi-simple over $k,$ and $G(k)$ the group of $k$-rational points of $G.$ Let $G(k)^+$ be the subgroup of $G(k)$ generated by the unipotent radicals of parabolic subgroups of $G$ defined over $k$ and $PG(k)^+$ the quotient of $G(k)^+$ by its center. Then every normalized function of positive type on $PG(k)^+$ which is constant on conjugacy classes is a convex combination of $1_{PG(k)^+}$ and $\\delta_e.$ As corollary, we obtain that the only ergodic invariant random su"},"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":"1908.06928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-19T16:56:58Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"18dfd41ea616eb9e4e7192cbd4cdf9c61561228b41d9a92a4c4f3c07f4848622","abstract_canon_sha256":"33719d4460e8ac5cc1a76591576eed67e017dc8e491d4c6dec831b475785f42c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:02:27.629064Z","signature_b64":"0sJChb+8LPudrDid+CB/oFUZ7yGE+MCWyQoXBdx+eAnuCjZelnP771crGhcwBxoifrweTMi+gRuX8TcBVGlWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eb6eb914a21c9f7a05c455cd068d95a7f9cf84f2fa803ea76121b0dbd673e10","last_reissued_at":"2026-07-05T01:02:27.628624Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:02:27.628624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Character rigidity of simple algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Bachir Bekka","submitted_at":"2019-08-19T16:56:58Z","abstract_excerpt":"We prove the following extension of Tits' simplicity theorem. Let $k$ be an infinite field, $G$ an algebraic group defined and quasi-simple over $k,$ and $G(k)$ the group of $k$-rational points of $G.$ Let $G(k)^+$ be the subgroup of $G(k)$ generated by the unipotent radicals of parabolic subgroups of $G$ defined over $k$ and $PG(k)^+$ the quotient of $G(k)^+$ by its center. Then every normalized function of positive type on $PG(k)^+$ which is constant on conjugacy classes is a convex combination of $1_{PG(k)^+}$ and $\\delta_e.$ As corollary, we obtain that the only ergodic invariant random su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06928","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/1908.06928/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":"1908.06928","created_at":"2026-07-05T01:02:27.628687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06928v2","created_at":"2026-07-05T01:02:27.628687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06928","created_at":"2026-07-05T01:02:27.628687+00:00"},{"alias_kind":"pith_short_12","alias_value":"P23OXEKKEHE7","created_at":"2026-07-05T01:02:27.628687+00:00"},{"alias_kind":"pith_short_16","alias_value":"P23OXEKKEHE7PIC4","created_at":"2026-07-05T01:02:27.628687+00:00"},{"alias_kind":"pith_short_8","alias_value":"P23OXEKK","created_at":"2026-07-05T01:02:27.628687+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/P23OXEKKEHE7PIC4IVONA2GZLJ","json":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ.json","graph_json":"https://pith.science/api/pith-number/P23OXEKKEHE7PIC4IVONA2GZLJ/graph.json","events_json":"https://pith.science/api/pith-number/P23OXEKKEHE7PIC4IVONA2GZLJ/events.json","paper":"https://pith.science/paper/P23OXEKK"},"agent_actions":{"view_html":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ","download_json":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ.json","view_paper":"https://pith.science/paper/P23OXEKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06928&json=true","fetch_graph":"https://pith.science/api/pith-number/P23OXEKKEHE7PIC4IVONA2GZLJ/graph.json","fetch_events":"https://pith.science/api/pith-number/P23OXEKKEHE7PIC4IVONA2GZLJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ/action/storage_attestation","attest_author":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ/action/author_attestation","sign_citation":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ/action/citation_signature","submit_replication":"https://pith.science/pith/P23OXEKKEHE7PIC4IVONA2GZLJ/action/replication_record"}},"created_at":"2026-07-05T01:02:27.628687+00:00","updated_at":"2026-07-05T01:02:27.628687+00:00"}