{"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. Let $H^0$ be its dual $C^*$-Hopf algebra. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09530","kind":"arxiv","version":1},"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"}