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We show that the C*-envelope of a semicrossed product is (a full corner of) a crossed product. As a consequence, we get that, when $\\alpha$ is *-injective, the semicrossed products are completely isometrically isomorphic and share the same C*-envelope, the crossed product $\\mathcal{C}_\\infty \\rtimes_{\\alpha_\\infty} \\mathbb{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":"1102.2252","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-10T22:36:57Z","cross_cats_sorted":[],"title_canon_sha256":"239d451960bd3d23e1abbd76bf9482c128180a8616f21f2d9707e0a68ceacdfa","abstract_canon_sha256":"6f02a4206f97788ddcc51575b499257bfec477cccb8bbe5ca7b5282b223671d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:01.164637Z","signature_b64":"aDCiWSmYpWdsNWrxH2nbOUxxPL+MHFTZoKoymW0Rml9qpHBxeUTB7rzB6LMDRqUGhkEKbWdTpdJRmA5b2RY6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a519a6beeefe26874ffa7cc8f9c5616f831a286e5aac1a7889bd20c537a164fa","last_reissued_at":"2026-05-18T00:08:01.164005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:01.164005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semicrossed products of C*-algebras and their C*-envelopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Evgenios T. A. Kakariadis","submitted_at":"2011-02-10T22:36:57Z","abstract_excerpt":"Let $\\mathcal{C}$ be a C*-algebra and $\\alpha:\\mathcal{C} \\rightarrow \\mathcal{C}$ a unital *-endomorphism. There is a natural way to construct operator algebras which are called semicrossed products, using a convolution induced by the action of $\\alpha$ on $\\mathcal{C}$. We show that the C*-envelope of a semicrossed product is (a full corner of) a crossed product. As a consequence, we get that, when $\\alpha$ is *-injective, the semicrossed products are completely isometrically isomorphic and share the same C*-envelope, the crossed product $\\mathcal{C}_\\infty \\rtimes_{\\alpha_\\infty} \\mathbb{Z}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2252","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":"1102.2252","created_at":"2026-05-18T00:08:01.164093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.2252v4","created_at":"2026-05-18T00:08:01.164093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2252","created_at":"2026-05-18T00:08:01.164093+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUM2NPXO7YTI","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUM2NPXO7YTIOT72","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUM2NPXO","created_at":"2026-05-18T12:26:42.757692+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/UUM2NPXO7YTIOT72PTEPTRLBN6","json":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6.json","graph_json":"https://pith.science/api/pith-number/UUM2NPXO7YTIOT72PTEPTRLBN6/graph.json","events_json":"https://pith.science/api/pith-number/UUM2NPXO7YTIOT72PTEPTRLBN6/events.json","paper":"https://pith.science/paper/UUM2NPXO"},"agent_actions":{"view_html":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6","download_json":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6.json","view_paper":"https://pith.science/paper/UUM2NPXO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.2252&json=true","fetch_graph":"https://pith.science/api/pith-number/UUM2NPXO7YTIOT72PTEPTRLBN6/graph.json","fetch_events":"https://pith.science/api/pith-number/UUM2NPXO7YTIOT72PTEPTRLBN6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6/action/storage_attestation","attest_author":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6/action/author_attestation","sign_citation":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6/action/citation_signature","submit_replication":"https://pith.science/pith/UUM2NPXO7YTIOT72PTEPTRLBN6/action/replication_record"}},"created_at":"2026-05-18T00:08:01.164093+00:00","updated_at":"2026-05-18T00:08:01.164093+00:00"}