Geodesic
A classification theorem for nuclear purely infinite simple $C^*$-algebras
Documenta mathematica, Tome 5 (2000), pp. 49-114.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Starting from Kirchberg's theorems announced at the operator algebra conference in Genève in 1994, namely ${\cal O}_{2} \otimes A \cong {\cal O}_{2}$ for separable unital nuclear simple $A$ and ${\cal O}_{\infty} \otimes {A} \cong A$ 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 $K_0$-class of the identity, then $A \cong B.$
Classification : 46L35, 19K99, 46L80 
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     title = {A classification theorem for nuclear purely infinite simple $C^*$-algebras},
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Phillips, N.Christopher. A classification theorem for nuclear purely infinite simple $C^*$-algebras. Documenta mathematica, Tome 5 (2000), pp. 49-114. http://geodesic.mathdoc.fr/item/DOCMA_2000__5__a17/