{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:34EKPU44V55YBGZRF6I4I2EV3I","short_pith_number":"pith:34EKPU44","schema_version":"1.0","canonical_sha256":"df08a7d39caf7b809b312f91c46895da3a15d55f9d26bb37e2ae9cb9bedebe0c","source":{"kind":"arxiv","id":"1104.2304","version":2},"attestation_state":"computed","paper":{"title":"On inverse semigroup $C^*$-algebras and crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Benjamin Steinberg, David Milan","submitted_at":"2011-04-12T18:58:06Z","abstract_excerpt":"We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the $C^*$-algebra of the tight groupoid of an inverse semigroup. We also study conditions on a groupoid $C^*$-algebra to be Morita equivalent to a full crossed product of a commutative $C^*$-algebra with an inverse semigroup, generalizing results of Khoshkam and Skandalis for crossed products with groups."},"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":"1104.2304","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-04-12T18:58:06Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"33a4688c45c7db1e42ae3fa2572e8c2e20a363ef0ecad7842352ac381474c152","abstract_canon_sha256":"fa5ef25d5e73b91162a26645e3f4423d3eb471895127cb5270ff69253da9dc09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:16.588365Z","signature_b64":"MBv0g/asmREFPLg6vBFOSDuENwH2I6DTEX0i6lNfmh5PL3iMVjKPTjSL0dPU8l27sx7Z3IXH22bsRBw1igfvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df08a7d39caf7b809b312f91c46895da3a15d55f9d26bb37e2ae9cb9bedebe0c","last_reissued_at":"2026-05-18T01:25:16.587691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:16.587691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On inverse semigroup $C^*$-algebras and crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Benjamin Steinberg, David Milan","submitted_at":"2011-04-12T18:58:06Z","abstract_excerpt":"We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the $C^*$-algebra of the tight groupoid of an inverse semigroup. We also study conditions on a groupoid $C^*$-algebra to be Morita equivalent to a full crossed product of a commutative $C^*$-algebra with an inverse semigroup, generalizing results of Khoshkam and Skandalis for crossed products with groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2304","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":""},"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":"1104.2304","created_at":"2026-05-18T01:25:16.587784+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.2304v2","created_at":"2026-05-18T01:25:16.587784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2304","created_at":"2026-05-18T01:25:16.587784+00:00"},{"alias_kind":"pith_short_12","alias_value":"34EKPU44V55Y","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"34EKPU44V55YBGZR","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"34EKPU44","created_at":"2026-05-18T12:26:18.847500+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/34EKPU44V55YBGZRF6I4I2EV3I","json":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I.json","graph_json":"https://pith.science/api/pith-number/34EKPU44V55YBGZRF6I4I2EV3I/graph.json","events_json":"https://pith.science/api/pith-number/34EKPU44V55YBGZRF6I4I2EV3I/events.json","paper":"https://pith.science/paper/34EKPU44"},"agent_actions":{"view_html":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I","download_json":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I.json","view_paper":"https://pith.science/paper/34EKPU44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.2304&json=true","fetch_graph":"https://pith.science/api/pith-number/34EKPU44V55YBGZRF6I4I2EV3I/graph.json","fetch_events":"https://pith.science/api/pith-number/34EKPU44V55YBGZRF6I4I2EV3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I/action/storage_attestation","attest_author":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I/action/author_attestation","sign_citation":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I/action/citation_signature","submit_replication":"https://pith.science/pith/34EKPU44V55YBGZRF6I4I2EV3I/action/replication_record"}},"created_at":"2026-05-18T01:25:16.587784+00:00","updated_at":"2026-05-18T01:25:16.587784+00:00"}