{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6LOUNA2JZN4MGBQAIHTF57FWGX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8ea6ef49dea62d2f625b1e32170cd344003160097ae04a46017083538c726c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T17:37:02Z","title_canon_sha256":"8ebea93c94d69bae893896598f672da06ef574543133504291298424d6c86633"},"schema_version":"1.0","source":{"id":"1402.3233","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3233","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3233v3","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3233","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"6LOUNA2JZN4M","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6LOUNA2JZN4MGBQA","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6LOUNA2J","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:5e05b869b4e48251d2e8c98aa022f941fe82fea68f5b319d2f706cc73af4f84a","target":"graph","created_at":"2026-05-18T01:29:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article we study simplicity and traces of reduced $L^p$ operator crossed products $F^p_{\\mathrm{r}}(G, A, \\alpha)$. Given $p \\in (1, \\infty)$, let $G$ be a Powers group, and let $\\alpha \\colon G \\to Aut(A)$ be an isometric action of $G$ on a unital $L^p$ operator algebra $A$ such that $A$ is $G$-simple. We prove that the reduced $L^p$ operator crossed product of $A$ by $G$, $F^p_{\\mathrm{r}}(G, A, \\alpha)$, is simple. Moreover, we show that traces on $F^p_{\\mathrm{r}}(G, A, \\alpha)$ are in correspondence with $G$-invariant traces on A. Our results generalize the results obtained by de ","authors_text":"Sanaz Pooya, Shirin Hejazian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T17:37:02Z","title":"Simple reduced $L^p$ operator crossed products with unique trace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3233","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b77ea8b72fee544015f3782c91f13c99f4925a72cd57fb431194f5b8d7b5dcfc","target":"record","created_at":"2026-05-18T01:29:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8ea6ef49dea62d2f625b1e32170cd344003160097ae04a46017083538c726c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-13T17:37:02Z","title_canon_sha256":"8ebea93c94d69bae893896598f672da06ef574543133504291298424d6c86633"},"schema_version":"1.0","source":{"id":"1402.3233","kind":"arxiv","version":3}},"canonical_sha256":"f2dd468349cb78c3060041e65efcb635ec6997a8e1b9b94bb58cebcbf8319c0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2dd468349cb78c3060041e65efcb635ec6997a8e1b9b94bb58cebcbf8319c0b","first_computed_at":"2026-05-18T01:29:59.596871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:59.596871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BYnsBbE1sH6BpB/QULJl39rd8lRv3prWg8TwLy7XK9XVdhJvWYyHhzjUUHU0nSC9ASVPZic5YaXL9MBzzNqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:59.597530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3233","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b77ea8b72fee544015f3782c91f13c99f4925a72cd57fb431194f5b8d7b5dcfc","sha256:5e05b869b4e48251d2e8c98aa022f941fe82fea68f5b319d2f706cc73af4f84a"],"state_sha256":"3ed223eef56303c7ff23c483e095cca5093553c7dcde7a36e9885cd1b2cfa8d7"}