{"paper":{"title":"Homomorphisms from AH-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Huaxin Lin","submitted_at":"2011-02-22T21:40:21Z","abstract_excerpt":"Let $C$ be a general unital AH-algebra and let $A$ be a unital simple $C^*$-algebra with tracial rank at most one. Suppose that $\\phi, \\psi: C\\to A$ are two unital monomorphisms. We show that $\\phi$ and $\\psi$ are approximately unitarily equivalent if and only if \\beq[\\phi]&=&[\\psi] {\\rm in} KL(C,A), \\phi_{\\sharp}&=&\\psi_{\\sharp}\\tand \\phi^{\\dag}&=&\\psi^{\\dag}, \\eneq where $\\phi_{\\sharp}$ and $\\psi_{\\sharp}$ are continuous affine maps from tracial state space $T(A)$ of $A$ to faithful tracial state space $T_{\\rm f}(C)$ of $C$ induced by $\\phi$ and $\\psi,$ respectively, and $\\phi^{\\ddag}$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4631","kind":"arxiv","version":6},"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"}