{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:GLI5QWCO7S4NKYTSVMSPCKAKPB","short_pith_number":"pith:GLI5QWCO","schema_version":"1.0","canonical_sha256":"32d1d8584efcb8d56272ab24f1280a787ef99227e66bf9df3d258f0d5707cff4","source":{"kind":"arxiv","id":"math/0702775","version":4},"attestation_state":"computed","paper":{"title":"Realization of minimal C*-dynamical systems in terms of Cuntz-Pimsner algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Ezio Vasselli, Fernando Lled\\'o","submitted_at":"2007-02-26T13:32:10Z","abstract_excerpt":"In the present paper we study tensor C*-categories with non-simple unit realised as C*-dynamical systems (F,G,\\beta) with a compact (non-Abelian) group G and fixed point algebra A := F^G. We consider C*-dynamical systems with minimal relative commutant of A in F, i.e. A' \\cap F = Z, where Z is the center of A which we assume to be nontrivial. We give first several constructions of minimal C*-dynamical systems in terms of a single Cuntz-Pimsner algebra associated to a suitable Z-bimodule. These examples are labelled by the action of a discrete Abelian group (which we call the chain group) on Z "},"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":"math/0702775","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2007-02-26T13:32:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c20d9fa34c17c7f47e88838e84bee9896330114eac416d8771cb846e9eed1937","abstract_canon_sha256":"817bc35bdc32fad23b9465145f5478ebdf96c550491b3887c45e3b66862e3dc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:05.419619Z","signature_b64":"zLEoQ6ARnN1pxmwaOTk9aafXotFmpvHEV983YP00QwZ154Nl1U+8Jbm8RKUXpNp5MrzmrUxyHceWSrE89YaLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32d1d8584efcb8d56272ab24f1280a787ef99227e66bf9df3d258f0d5707cff4","last_reissued_at":"2026-05-18T04:08:05.418834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:05.418834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Realization of minimal C*-dynamical systems in terms of Cuntz-Pimsner algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Ezio Vasselli, Fernando Lled\\'o","submitted_at":"2007-02-26T13:32:10Z","abstract_excerpt":"In the present paper we study tensor C*-categories with non-simple unit realised as C*-dynamical systems (F,G,\\beta) with a compact (non-Abelian) group G and fixed point algebra A := F^G. We consider C*-dynamical systems with minimal relative commutant of A in F, i.e. A' \\cap F = Z, where Z is the center of A which we assume to be nontrivial. We give first several constructions of minimal C*-dynamical systems in terms of a single Cuntz-Pimsner algebra associated to a suitable Z-bimodule. These examples are labelled by the action of a discrete Abelian group (which we call the chain group) on Z "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702775","kind":"arxiv","version":4},"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":"math/0702775","created_at":"2026-05-18T04:08:05.418961+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0702775v4","created_at":"2026-05-18T04:08:05.418961+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702775","created_at":"2026-05-18T04:08:05.418961+00:00"},{"alias_kind":"pith_short_12","alias_value":"GLI5QWCO7S4N","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"GLI5QWCO7S4NKYTS","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"GLI5QWCO","created_at":"2026-05-18T12:25:55.427421+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/GLI5QWCO7S4NKYTSVMSPCKAKPB","json":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB.json","graph_json":"https://pith.science/api/pith-number/GLI5QWCO7S4NKYTSVMSPCKAKPB/graph.json","events_json":"https://pith.science/api/pith-number/GLI5QWCO7S4NKYTSVMSPCKAKPB/events.json","paper":"https://pith.science/paper/GLI5QWCO"},"agent_actions":{"view_html":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB","download_json":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB.json","view_paper":"https://pith.science/paper/GLI5QWCO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0702775&json=true","fetch_graph":"https://pith.science/api/pith-number/GLI5QWCO7S4NKYTSVMSPCKAKPB/graph.json","fetch_events":"https://pith.science/api/pith-number/GLI5QWCO7S4NKYTSVMSPCKAKPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB/action/storage_attestation","attest_author":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB/action/author_attestation","sign_citation":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB/action/citation_signature","submit_replication":"https://pith.science/pith/GLI5QWCO7S4NKYTSVMSPCKAKPB/action/replication_record"}},"created_at":"2026-05-18T04:08:05.418961+00:00","updated_at":"2026-05-18T04:08:05.418961+00:00"}