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Let $(\\rho, u)$ and $(\\sigma, v)$ be twisted coactions of $H^0$ on $A$ and $B$, respectively. In this paper, we shall show the following theorem: We suppose that the unital inclusions $A\\subset A\\rtimes_{\\rho, u}H$ and $B\\subset B\\rtimes_{\\sigma, v}H$ are strongly Morita equivalent. If $A'\\cap (A\\rtimes_{\\rho, u}H)=\\BC1$, then there is a $C^*$-Hopf algebra automorphism $\\lambda^0$ of $H^0$ such that the twisted coaction $(\\rho, u)$ is strongly Morita equiva"},"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":"1706.09530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-29T00:56:29Z","cross_cats_sorted":[],"title_canon_sha256":"77aac08328d028fcaa5bff0fe81d3f0c55233949f086fd5c0778e2c0ed4d4a74","abstract_canon_sha256":"22de41847471cb52609c0a1a85f8b2b2f792a4451967c6676566ad4e4c6d19fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:14.825547Z","signature_b64":"a+O1KfIo2+q4u7wfnyrZAOItySWspzQBZfoiWPSJx7/Tw2Y7LAXn4p+X8Ti0BXGTv45DADw9P+WCJVl021QoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f2ceba17b772a1d8f528e5bd1ea2ba8c6026307ed9ac4e2667cda17892dad9c","last_reissued_at":"2026-05-18T00:41:14.824863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:14.824863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coactions of a finite dimensional $C^*$-Hopf algebra on unital $C^*$-algebras, unital inclusions of unital $C^*$-algebras and the strong Morita equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Kazunori Kodaka, Tamotsu Teruya","submitted_at":"2017-06-29T00:56:29Z","abstract_excerpt":"Let $A$ and $B$ be unital $C^*$-algebras and let $H$ be a finite dimensional $C^*$-Hopf algebra. 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