{
  "annotation_id": "63c24c54-8e58-40b3-ae90-61888ace6ad2",
  "date_created": "2026-02-17T05:53:15.716000Z",
  "date_modified": "2026-02-17T05:53:15.716000Z",
  "file_hash": "955d5fec1e8d21ff5a27a436a1f511244169fad96499013dac995699728d55dc",
  "private": false,
  "record": {
    "abstract": "Let $A$ be a separable, unital and exact $C^*$-algebra satisfying the universal coefficient theorem. We prove uniqueness theorems up to unitary conjugacy for unital, full and nuclear maps from $A$ into ultraproducts of finite von Neumann factors: any two such maps agreeing on traces and total $K$-theory are unitarily equivalent. There are two consequences. Firstly if one takes the factors to be a sequence $(M_{k_n})_{n}$ of matrix algebras, we obtain a uniqueness result for quasidiagonal approximations of $A$. Secondly, when $(\\mathcal M,\\tau_{\\calM})$ is a II$_1$ factor, a pair $\\phi,\\psi:A\\to\\mathcal M$ of unital, injective and nuclear maps are norm approximately unitarily equivalent if and only if $\\tau_{\\calM}\\circ\\phi=\\tau_{\\calM}\\circ\\psi$.\n  The main strategy is to use Schafhauser\u0027s classification of lifts along the trace--kernel extension. Since our codomains may lack the tensorial absorption properties needed in this work, the main new ingredient is a suitable $KK$-uniqueness theorem tailored to our situation. This is inspired by $KK$-uniqueness theorems of Loreaux, Ng and Sutradhar.",
    "arxiv_id": "2601.08779",
    "authors": [
      "Shanshan Hua",
      "Stuart White"
    ],
    "categories": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Uniqueness for embeddings of nuclear $C^*$-algebras into type II$_{1}$ factors",
    "url": "https://arxiv.org/abs/2601.08779",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6bec7d4b-0540-4bcf-bf54-9010ada07a5a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}