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We prove that the partial-isometric crossed product $A\\times_{\\alpha}^{\\textrm{piso}}\\Gamma^{+}$ is a full corner of a group crossed product $\\mathcal{B}\\times_{\\beta}\\Gamma$, where $\\mathcal{B}$ is a subalgebra of $\\ell^{\\infty}(\\Gamma,A)$ generated by a collection of faithful copies of $A$, and the action $\\beta$ on $\\mathcal{B}$ is induced by shift on $\\ell^{\\infty}(\\Gamma,A)$. We then use this realization to s"},"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":"1710.06708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-10-18T12:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"6937d3251dff03bc17274aec30107e30ab0f769f2ab9a73aea8e8d8462831cd1","abstract_canon_sha256":"84ab99d9b6b531ae382ef62ae04f612abeacf13cc3ec014ad40e4f4c04b505b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:32.904347Z","signature_b64":"Zhe1/TEYgVky0tISbVT5IJCwLkWXGkpsNW9bAKKD+mjyQJXCX80N9ooL8LA2dv3McpgpDg4Ot0brgjFD/0B3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f21c41e4a2fbe480ae4e278ccf28348de5690a927aa6c6832ecced7ba597839","last_reissued_at":"2026-05-18T00:32:32.903823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:32.903823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The partial-isometric crossed products by semigroups of endomorphisms are Morita equivalent to crossed products by groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Saeid Zahmatkesh","submitted_at":"2017-10-18T12:55:24Z","abstract_excerpt":"Let $\\Gamma^{+}$ be the positive cone of a totally ordered abelian discrete group $\\Gamma$, and $\\alpha$ an action of $\\Gamma^{+}$ by extendible endomorphisms of a $C^*$-algebra $A$. We prove that the partial-isometric crossed product $A\\times_{\\alpha}^{\\textrm{piso}}\\Gamma^{+}$ is a full corner of a group crossed product $\\mathcal{B}\\times_{\\beta}\\Gamma$, where $\\mathcal{B}$ is a subalgebra of $\\ell^{\\infty}(\\Gamma,A)$ generated by a collection of faithful copies of $A$, and the action $\\beta$ on $\\mathcal{B}$ is induced by shift on $\\ell^{\\infty}(\\Gamma,A)$. 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