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arxiv: 2202.04695 · v2 · pith:ISJJIPZQnew · submitted 2022-02-09 · 🧮 math.OA

The nuclear dimension of extensions of commutative C*-algebras by the compact operators

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keywords dimensionalgebracompactnuclearoperatorsalgebrasbrakecase
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Generalizing the case of the Toeplitz algebra by Brake and Winter, we prove that the nuclear dimension of a C*-algebra extension of C(X) by the compact operators is equal to the dimension of X.

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  1. Uniqueness for embeddings of nuclear $C^*$-algebras into type II$_{1}$ factors

    math.OA 2026-01 unverdicted novelty 7.0

    Uniqueness up to unitary conjugacy holds for nuclear maps from separable exact C*-algebras satisfying the UCT into ultraproducts of finite factors when the maps agree on traces and total K-theory.