{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ZW4XRRXKZTXRMHCWBKEMBYR62L","short_pith_number":"pith:ZW4XRRXK","schema_version":"1.0","canonical_sha256":"cdb978c6eaccef161c560a88c0e23ed2ffe88995f0dc70e15fb7b526d9c5d674","source":{"kind":"arxiv","id":"2403.13645","version":3},"attestation_state":"computed","paper":{"title":"Maximal ideals of reduced group C*-algebras and Thompson's groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Chris Bruce, Eduardo Scarparo, Kang Li, Kevin Aguyar Brix","submitted_at":"2024-03-20T14:52:11Z","abstract_excerpt":"Given a conditional expectation $P$ from a C*-algebra $B$ onto a C*-subalgebra $A$, we observe that induction of ideals via $P$, together with a map which we call co-induction, forms a Galois connection between the lattices of ideals of $A$ and $B$. Using properties of this Galois connection, we show that, given a discrete group $G$ and a stabilizer subgroup $G_x$ for the action of $G$ on its Furstenberg boundary, induction gives a bijection between the set of maximal co-induced ideals of $C^*(G_x)$ and the set of maximal ideals of $C^*_r(G)$.\n  As an application, we prove that the reduced C*-"},"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":"2403.13645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-03-20T14:52:11Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"188dd7094aaf27b044e1b0fa2b5ceaa09ab014bb68bf1a81c0ad51e1bb040303","abstract_canon_sha256":"0d167b0ca9dd91b859b2fea6291a4053e39e7e0ec30ed6174fabcfc421c9cea9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:42.030535Z","signature_b64":"CevP3cAtbuWxGiTrAHeSrx2/o7uhAM3YwkLnPjHxpAPuEtn4DXsKwSUImblXgK8rgqracseDQptSUuqoG8RxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdb978c6eaccef161c560a88c0e23ed2ffe88995f0dc70e15fb7b526d9c5d674","last_reissued_at":"2026-06-26T01:15:42.030012Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:42.030012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal ideals of reduced group C*-algebras and Thompson's groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Chris Bruce, Eduardo Scarparo, Kang Li, Kevin Aguyar Brix","submitted_at":"2024-03-20T14:52:11Z","abstract_excerpt":"Given a conditional expectation $P$ from a C*-algebra $B$ onto a C*-subalgebra $A$, we observe that induction of ideals via $P$, together with a map which we call co-induction, forms a Galois connection between the lattices of ideals of $A$ and $B$. Using properties of this Galois connection, we show that, given a discrete group $G$ and a stabilizer subgroup $G_x$ for the action of $G$ on its Furstenberg boundary, induction gives a bijection between the set of maximal co-induced ideals of $C^*(G_x)$ and the set of maximal ideals of $C^*_r(G)$.\n  As an application, we prove that the reduced C*-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.13645","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.13645/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":"2403.13645","created_at":"2026-06-26T01:15:42.030070+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.13645v3","created_at":"2026-06-26T01:15:42.030070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.13645","created_at":"2026-06-26T01:15:42.030070+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZW4XRRXKZTXR","created_at":"2026-06-26T01:15:42.030070+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZW4XRRXKZTXRMHCW","created_at":"2026-06-26T01:15:42.030070+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZW4XRRXK","created_at":"2026-06-26T01:15:42.030070+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/ZW4XRRXKZTXRMHCWBKEMBYR62L","json":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L.json","graph_json":"https://pith.science/api/pith-number/ZW4XRRXKZTXRMHCWBKEMBYR62L/graph.json","events_json":"https://pith.science/api/pith-number/ZW4XRRXKZTXRMHCWBKEMBYR62L/events.json","paper":"https://pith.science/paper/ZW4XRRXK"},"agent_actions":{"view_html":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L","download_json":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L.json","view_paper":"https://pith.science/paper/ZW4XRRXK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.13645&json=true","fetch_graph":"https://pith.science/api/pith-number/ZW4XRRXKZTXRMHCWBKEMBYR62L/graph.json","fetch_events":"https://pith.science/api/pith-number/ZW4XRRXKZTXRMHCWBKEMBYR62L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L/action/storage_attestation","attest_author":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L/action/author_attestation","sign_citation":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L/action/citation_signature","submit_replication":"https://pith.science/pith/ZW4XRRXKZTXRMHCWBKEMBYR62L/action/replication_record"}},"created_at":"2026-06-26T01:15:42.030070+00:00","updated_at":"2026-06-26T01:15:42.030070+00:00"}