{"paper":{"title":"A Non-Commutative Unitary Analogue of Kirchberg's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Samuel J. Harris","submitted_at":"2016-08-10T16:18:09Z","abstract_excerpt":"The $C^{\\ast}$-algebra $\\mathcal{U}_{nc}(n)$ is the universal $C^{\\ast}$-algebra generated by $n^2$ generators $u_{ij}$ that make up a unitary matrix. We prove that Kirchberg's formulation of Connes' embedding problem has a positive answer if and only if $\\mathcal{U}_{nc}(2) \\otimes_{\\min} \\mathcal{U}_{nc}(2)=\\mathcal{U}_{nc}(2) \\otimes_{\\max} \\mathcal{U}_{nc}(2)$. Our results follow from properties of the finite-dimensional operator system $\\mathcal{V}_n$ spanned by $1$ and the generators of $\\mathcal{U}_{nc}(n)$. We show that $\\mathcal{V}_n$ is an operator system quotient of $M_{2n}$ and has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03229","kind":"arxiv","version":3},"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"}