Embedding of Exact C*-algebras and Continuous Fields in the Cuntz Algebra O 2

@inproceedings{Phillips2008EmbeddingOE,
  title={Embedding of Exact C*-algebras and Continuous Fields in the Cuntz Algebra O 2},
  author={N. C. Phillips},
  year={2008}
}
We prove that any separable exact C*-algebra is isomorphic to a subalgebra of the Cuntz algebra O 2. We further prove that if A is a simple separable unital nuclear C*-algebra, then O 2 ⊗ A ∼ = O 2 , and if, in addition, A is purely infinite, then O∞ ⊗ A ∼ = A. The embedding of exact C*-algebras in O 2 is continuous in the following sense. If A is a continuous field of C*-algebras over a compact manifold or finite CW complex X with fiber A(x) over x ∈ X, such that the algebra of continuous… CONTINUE READING
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