Geodesic
A classification theorem for nuclear purely infinite simple $C^*$-algebras
Documenta mathematica, Tome 5 (2000), pp. 49-114
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Starting from Kirchberg's theorems announced at the operator algebra conference in Genève in 1994, namely O2​⊗A≅O2​ for separable unital nuclear simple A and O∞​⊗A≅A for separable unital nuclear purely infinite simple A, we prove that KK-equivalence implies isomorphism for nonunital separable nuclear purely infinite simple C∗-algebras. It follows that if A and B are unital separable nuclear purely infinite simple C∗-algebras which satisfy the Universal Coefficient Theorem, and if there is a graded isomorphism from K∗​(A) to K∗​(B) which preserves the K0​-class of the identity, then A≅B.
DOI : 10.4171/dm/75
Classification : 19K99, 46L35, 46L80 
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     title = {A classification theorem for nuclear purely infinite simple $C^*$-algebras},
     journal = {Documenta mathematica},
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N.Christopher Phillips. A classification theorem for nuclear purely infinite simple $C^*$-algebras. Documenta mathematica, Tome 5 (2000), pp. 49-114. doi: 10.4171/dm/75

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