{"paper":{"title":"Equivariant Picard groups of $C^*$-algebras with finite dimensional $C^*$-Hopf algebra coactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Kazunori Kodaka","submitted_at":"2015-12-24T06:13:05Z","abstract_excerpt":"Let $A$ be a $C^*$-algebra and $H$ a finite dimensional $C^*$-Hopf algebra with its dual $C^*$-Hopf algebra $H^0$. Let $(\\rho, u)$ be a twisted coaction of $H^0$ on $A$. We shall define the $(\\rho, u, H)$-equivariant Picard group of $A$, which is denoted by $\\Pic_H^{\\rho, u}(A)$, and discuss basic properties of $\\Pic_H^{\\rho, u}(A)$. Also, we suppose that $(\\rho, u)$ is the coaction of $H^0$ on the unital $C^*$-algebra $A$, that is, $u=1\\otimes 1^0$. We investigate the relation between $\\Pic(A^s )$, the ordinary Picard group of $A^s$ and $\\Pic_H^{\\rho^s}(A^s )$ where $A^s$ is the stable $C^*$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07724","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"}